#MATH 221 Statistics for Decision Making Week 6 iLab | Explore Tumblr posts and blogs

hwcampus · 8 years ago

Text

New Post has been published on Online Professional Homework Help

New Post has been published on http://hwcampus.com/shop/math-221-entire-course/

MATH 221 Entire Course

MATH 221 Entire Course Statistics for Decision-Making

MATH 221 Entire Course Statistics for Decision-Making NEW This Course Includes ALL iLabs, Homework, Quizzes, Final Exam, and All Discussions Week 3 Quiz – 3 Sets Week 5 Quiz – 3 Sets Week 7 Quiz 4 Sets

Statistical Concepts that you will learn after completing this iLab: • Using Excel for Statistics • Graphics • Shapes of Distributions • Descriptive Statistics • Empirical Rule Week 2 iLab Instructions-BEGIN • Data have already been formatted and entered into an Excel worksheet. • Obtain the data file for this lab from your instructor. • The names of each variable from the survey are in the first row of the Worksheet. This row has a background color of gray to identify it as the variable names. All other rows of the Worksheet represent a certain students’ answers to the survey questions. Therefore, the rows are called observations and the columns are called variables. On page 6 of this lab, you will find a code sheet that identifies the correspondence between the variable names and the survey questions. • Follow the directions below and then paste the graphs from Excel in the grey areas for question 1 through 3. Type your answers to questions 4 through 11 where noted in the grey areas. When asked for explanations, please give thorough, multi-sentence or paragraph length explanations. • PLEASE NOTE that various versions of Excel may have slightly different formula commands. For example, some versions use =STDEV.S while other versions would use =STDEVS (without the dot before the last “S”). • The completed iLab Word Document with your responses to the 11 questions will be the ONE and only document submitted to the dropbox. When saving and submitting the document, you are required to use the following format: Last Name_ First Name_Week2iLab. Week 2 iLab Instructions-END Creating Graphs Create a pie chart for the variable Car Color: Select the column with the Car variable, including the title of Car Color. Click on Insert, and then Recommended Charts. It should show a clustered column and click OK. Once the chart is shown, right click on the chart (main area) and select Change Chart Type. Select Pie and OK. Click on the pie slices, right click Add Data Labels, and select Add Data Callouts. Add an appropriate title. Copy and paste the chart here. (4 points) Create a histogram for the variable Height. You need to create a frequency distribution for the data by hand. Use 5 classes, find the class width, and then create the classes. Once you have the classes, count how many data points fall within each class. It may be helpful to sort the data based on the Height variable first. Create a new worksheet in Excel by clicking on the + along the bottom of the screen and type in the categories and the frequency for each category. Then select the frequency table, click on Insert, then Recommended Charts and choose the column chart shown and click OK. Right click on one of the bars and select Format Data Series. In the pop up box, change the Gap Width to 0. Add an appropriate title and axis label. Copy and paste the graph here. (4 points) 1. Type up a stem-and-leaf plot chart in the box below for the variable Money, with a space between the stems and the group of leaves in each line. Use the tens value as the stem and the ones value for the leaves. It may be helpful to sort the data based on the Money variable first. An example of a stem-and-leaf plot would look like this: • 4 5 6 9 3 • 5 6 3 6 • 9 2 The stem-and-leaf plot shown above would be for data 4, 5, 6, 9, 3, 15, 16, 13, 16, 29, and 22. (4 points) Calculating Descriptive Statistics 1. Calculate descriptive statistics for the variable Height by Gender. Click on Insert and then Pivot Table. Click in the top box and select all the data (including labels) from Height through Gender. Also click on “new worksheet” and then OK. On the right of the new sheet, click on Height and Gender, making sure that Gender is in the Rows box and Height is in the Values Click on the down arrow next to Height in the Values box and select Value Field Settings. In the pop up box, click Average then OK. Type in the averages below. Then click on the down arrow next to Height in the Values box again and select Value Field Settings. In the pop up box, click on StdDev then OK. Type the standard deviations below. (3 points) Short Answer Writing Assignment All answers should be complete sentences. What is the most common color of car for students who participated in this survey? Explain how you arrived at your answer. (5 points) What is seen in the histogram created for the heights of students in this class (include the shape)? Explain your answer. (5 points) What is seen in the stem and leaf plot for the money variable (include the shape)? Explain your answer. (5 points) Compare the mean for the heights of males and the mean for the heights of females in these data. Compare the values and explain what can be concluded based on the numbers. (5 points) Compare the standard deviation for the heights of males and the standard deviation for the heights of females in the class. Compare the values and explain what can be concluded based on the numbers. (5 points) Using the empirical rule, 95% of female heights should be between what two values? Either show work or explain how your answer was calculated. (5 points) Using the empirical rule, 68% of male heights should be between what two values? Either show work or explain how your answer was calculated. (5 points) MATH 221 iLab Week 4 NEW DeVry

Statistical Concepts: • Probability • Binomial Probability Distribution Calculating Binomial Probabilities • Open a new MINITAB worksheet. • We are interested in a binomial experiment with 10 trials. First, we will make the probability of a success ¼. Use MINITAB to calculate the probabilities for this distribution. In column C1 enter the word ‘success’ as the variable name (in the shaded cell above row 1. Now in that same column, enter the numbers zero through ten to represent all possibilities for the number of successes. These numbers will end up in rows 1 through 11 in that first column. In column C2 enter the words ‘one fourth’ as the variable name. Pull up Calc > Probability Distributions > Binomial and select the radio button that corresponds to Probability. Enter 10 for the Number of trials: and enter 0.25 for the Event probability:. For the Input column: select ‘success’ and for the Optional storage: select ‘one fourth’. Click the button OK and the probabilities will be displayed in the Worksheet. • Now we will change the probability of a success to ½. In column C3 enter the words ‘one half’ as the variable name. Use similar steps to that given above in order to calculate the probabilities for this column. The only difference is in Event probability: use 0.5. • Finally, we will change the probability of a success to ¾. In column C4 enter the words ‘three fourths’ as the variable name. Again, use similar steps to that given above in order to calculate the probabilities for this column. The only difference is in Event probability: use 0.75. Plotting the Binomial Probabilities 1. Create plots for the three binomial distributions above. Select Graph > Scatter Plot and Simple then for graph 1 set Y equal to ‘one fourth’ and X to ‘success’ by clicking on the variable name and using the “select” button below the list of variables. Do this two more times and for graph 2 set Y equal to ‘one half’ and X to ‘success’, and for graph 3 set Y equal to ‘three fourths’ and X to ‘success’. Paste those three scatter plots below. Calculating Descriptive Statistics • Open the class survey results that were entered into the MINITAB worksheet. 2. Calculate descriptive statistics for the variable where students flipped a coin 10 times. Pull up Stat > Basic Statistics > Display Descriptive Statistics and set Variables: to the coin. The output will show up in your Session Window. Type the mean and the standard deviation here. Short Answer Writing Assignment – Both the calculated binomial probabilities and the descriptive statistics from the class database will be used to answer the following questions. 3. List the probability value for each possibility in the binomial experiment that was calculated in MINITAB with the probability of a success being ½. (Complete sentence not necessary) 4. Give the probability for the following based on the MINITAB calculations with the probability of a success being ½. (Complete sentence not necessary) 5. Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being ½. Either show work or explain how your answer was calculated. Mean = np, Standard Deviation = 6. Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being ¼ and compare to the results from question 5. Mean = np, Standard Deviation = 7. Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being ¾ and compare to the results from question 6. Mean = np, Standard Deviation = 8. Explain why the coin variable from the class survey represents a binomial distribution. 9. Give the mean and standard deviation for the coin variable and compare these to the mean and standard deviation for the binomial distribution that was calculated in question 5. Explain how they are related. Mean = np, Standard Deviation = MATH 221 iLab Week 6 NEW DeVry

Statistical Concepts: • Data Simulation • Confidence Intervals • Normal Probabilities Short Answer Writing Assignment All answers should be complete sentences. We need to find the confidence interval for the SLEEP variable. To do this, we need to find the mean and then find the maximum error. Then we can use a calculator to find the interval, (x – E, x + E). First, find the mean. Under that column, in cell E37, type =AVERAGE (E2:E36). Under that in cell E38, type =STDEV (E2:E36). Now we can find the maximum error of the confidence interval. To find the maximum error, we use the “confidence” formula. In cell E39, type =CONFIDENCE.NORM (0.05, E38, 35). The 0.05 is based on the confidence level of 95%, the E38 is the standard deviation, and 35 is the number in our sample. You then need to calculate the confidence interval by using a calculator to subtract the maximum error from the mean (x-E) and add it to the mean (x+E). 1. Give and interpret the 95% confidence interval for the hours of sleep a student gets. (6 points) 2. Give and interpret the 99% confidence interval for the hours of sleep a student gets. (6 points) 3. Compare the 95% and 99% confidence intervals for the hours of sleep a student gets. Explain the difference between these intervals and why this difference occurs. (6 points) 4. Give and interpret the 95% confidence intervals for males and females on the HEIGHT variable. Which is wider and why? (9 points) 5. Give and interpret the 99% confidence intervals for males and females on the HEIGHT variable. Which is wider and why? (9 points) 6. Find the mean and standard deviation of the DRIVE variable by using =AVERAGE(A2:A36) and =STDEV(A2:A36). Assuming that this variable is normally distributed, what percentage of data would you predict would be less than 40 miles? This would be based on the calculated probability. Use the formula =NORM.DIST(40, mean, stdev,TRUE). Now determine the percentage of data points in the dataset that fall within this range. To find the actual percentage in the dataset, sort the DRIVE variable and count how many of the data points are less than 40 out of the total 35 data points. That is the actual percentage. How does this compare with your prediction? (12 points) 7. What percentage of data would you predict would be between 40 and 70 and what percentage would you predict would be more than 70 miles? Subtract the probabilities found through =NORM.DIST(70, mean, stdev, TRUE) and =NORM.DIST(40, mean, stdev, TRUE) for the “between” probability. To get the probability of over 70, use the same =NORM.DIST(70, mean, stdev, TRUE) and then subtract the result from 1 to get “more than”. Now determine the percentage of data points in the dataset that fall within this range, using same strategy as above for counting data points in the data set. How do each of these compare with your prediction and why is there a difference? (12 points) MATH 221 iLab Week 2 DeVry

Statistical Concepts: • Using Minitab • Graphics • Shapes of Distributions • Descriptive Statistics • Empirical Rule Data in Minitab • Minitab is a powerful, yet user-friendly, data analysis software package. You can launch Minitab by finding the icon and double clicking on it. After a moment you will see two windows, the Session Window in the top half of the screen and the Worksheet or Data Window in the bottom half. • Data have already been formatted and entered into a Minitab worksheet. Go to the eCollege Doc sharing site to download this data file. The names of each variable from the survey are in the first row of the Worksheet. This row has a background color of gray to identify it as the variable names. All other rows of the Minitab Worksheet represent a certain students’ answers to the survey questions. Therefore, the rows are called observations and the columns are called variables. Included with this lab, you will find a code sheet that identifies the correspondence between the variable names and the survey questions. • Complete the questions after the Code Sheet and paste the Graphs from Minitab in the grey areas for question 1 through 3. Type your answers to questions 4 through 11 where noted in the grey areas. When asked for explanations, please give thorough, multi-sentence or paragraph length explanations. The completed iLab Word Document with your responses to the questions will be the ONE and only document submitted to the dropbox. When saving and submitting the document, you are required to use the following format: Last Name_ First Name_Week2iLab. Code Sheet Do NOT answer these questions. The Code Sheet just lists the variables name and the question used by the researchers on the survey instrument that produced the data that are included in the Minitab data file. This is just information. The first question for the lab is after the code sheet…. MATH 221 iLab Week 4 DeVry

Statistical Concepts: • Data Simulation • Discrete Probability Distribution • Confidence Intervals Calculations for a set of variables • Open the class survey results that were entered into the MINITAB worksheet. • We want to calculate the mean for the 10 rolls of the die for each student in the class. Label the column next to die10 in the Worksheet with the word mean. Pull up Calc > Row Statistics and select the radio-button corresponding to Mean. For Input variables: enter all 10 rows of the die data. Go to the Store result in: and select the mean Click OK and the mean for each observation will show up in the Worksheet. • We also want to calculate the median for the 10 rolls of the die. Label the next column in the Worksheet with the word median. Repeat the above steps but select the radio-button that corresponds to Median and in the Store results in: text area, place the median Calculating Descriptive Statistics • Calculate descriptive statistics for the mean and median columns that where created above. Pull up Stat > Basic Statistics > Display Descriptive Statistics and set Variables: to mean and median. The output will show up in your Session Window. Print this information. Calculating Confidence Intervals for one Variable • Open the class survey results that were entered into the MINITAB worksheet. • We are interested in calculating a 95% confidence interval for the hours of sleep a student gets. Pull up Stat > Basic Statistics > 1-Sample t and set Samples in columns: to Sleep. Click the OK button and the results will appear in your Session Window. • We are also interested in the same analysis with a 99% confidence interval. Use the same steps except select the Options button and change the Confidence level: to 99. Short Answer Writing Assignment All answers should be complete sentences. MATH 221 Quiz Week 3 ALL Answers are 100% Correct 3 Sets

Choose the correct description of the population. A. The number of home owners in the state B. The income of home owners in the state who own a car C. The income of home owners in the state D. The number of home owners in the state who own a car Choose the correct description of the sample A. The income of home owners in the state who own a car B. The income of home owners in the state C. The number of home owners in the state who own a car D. The number of home owners in the state 2. Determine whether the variable is qualitative or quantitative. Favorite sport Is the variable qualitative or quantitative? A. Qualitative B. Quantitative 3. Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 30 students. The scores are shown below. 43 50 10 91 76 35 64 36 42 72 53 62 35 74 50 72 36 28 38 61 48 63 35 41 22 36 50 46 85 13 To find the 10% trimmed mean of a data set, order the data, delete the lowest 10% of the entries and highest 10% of the entries, and find the mean of the remaining entries. Complete parts (a) through (c). (a) Find the 10% trimmed mean for the data. The 10% trimmed mean is. (Round to the nearest tenth as needed.) (b) Compare the four measures of central tendency, including the midrange. Mean = (Round to the nearest tenth as needed.) Median = Mode = (Use a comma to separate answers as needed.) Midrange = (Round to the nearest tenth as needed.) (c) What is the benefit of using a trimmed mean versus using a mean found using all data entries? A. It simply decreases the number of computations in finding the mean. B. It permits the comparison of the measures of central tendency. C. It permits finding the mean of a data set more exactly. D. It eliminates potential outliers that could affect the mean of the entries. 4. Construct a frequency distribution for the given data set using 6 classes. In the table, include the midpoints, relative frequencies, and cumulative frequencies. Which class has the greatest frequency and which has the least frequency? Amount (in dollars) spent on books for a semester 457 146 287 535 442 543 46 405 496 385 517 56 33 132 64 99 378 145 30 419 336 228 376 227 262 340 172 116 285 Complete the table, starting with the lowest class limit. Use the minimum data entry as the lower limit of the first class. (Type integers or decimals rounded to the nearest thousandth as needed.)

Which class has the greatest frequency? The class with the greatest frequency is from to. Which class has the least frequency? The class with the least frequency is from to. 5. Identify the data set’s level of measurement. The nationalities listed in a recent survey (for example, American, German, or Brazilian) A. Nominal B. Ordinal C. Interval D. Ratio 6. Explain the relationship between variance and standard deviation. Can either of these measures be negative? Choose the correct answer below. A. The standard deviation is the negative square root of the variance. The standard deviation can be negative but the variance can never be negative. B. The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative. C. The variance is the negative square root of the standard deviation. The variance can be negative but the standard deviation can never be negative. D. The variance is the positive square root of the standard deviation. The standard deviation and variance can never be negative. Squared deviations can never be negative. 7. For the following data (a) display the data in a scatter plot, (b) calculate the correlation coefficient r, and (c) make a conclusion about the type of correlation. The number of hours 6 students watched television during the weekend and the scores of each student who took a test the following Monday. Hours spent watching TV, x 0 1 2 3 3 5 Test score, y 98 90 84 74 93 65 (a) Choose the correct scatter plot below.

(b) The correlation coefficient r is (Round to three decimal places as needed) (c) Which of the following best describes the type of correlation that exists between number of hours spent watching television and test scores? A. Strong negative linear correlation B. No linear correlation C. Weak negative linear correlation D. Strong positive linear correlation E. Weak positive linear correlation 8. Suppose a survey of 526 women in the United States found that more than 70% are the primary investor in their household. Which part of the survey represents the descriptive branch of statistics? Choose the best statement of the descriptive statistic in the problem. A. There is an association between the 526 women and being the primary investor in their household. B. 526 women were surveyed. C. 70% of women in the sample are the primary investor in their household. D. There is an association between U.S. women and being the primary investor in their household. Choose the best inference from the given information. A. There is an association between the 526 women and being the primary investor in their household. B. There is an association between U.S. women and being the primary investor in their household. C. 70% of women in the sample are the primary investor in their household D. 526 women were surveyed. 9. Identify the sampling technique used. A community college student interviews everyone in a particular statistics class to determine the percentage of students that own a car. A. Random B. Cluster C. Convenience D. Stratified E. Systematic 10. Use the frequency polygon to identify the class with the greatest, and the class with the least frequency.

What are the boundaries of the class with the greatest frequency? A. 25.5-30.5 B. 25-31 C. 26.5-29.5 D. 28-31 What are the boundaries of the class with the least frequency? A. 10-13 B. 5-11.5 C. 7-13 D. 5-12.5 11. Determine whether the given value is a statistic or a parameter In a study of all 2377 students at a college, it is found that 35% own a computer Choose the correct statement below. A. Parameter because the value is a numerical measurement describing a characteristic of a population. B. Statistic because the value is a numerical measurement describing a characteristic of a population. C. Statistic because the value is a numerical measurement describing a characteristic of a sample. D. Parameter because the value is a numerical measurement describing a characteristic of a sample. 12. Compare the three data sets

(a) Which data set has the greatest sample standard deviation? A. Data set (iii), because it has more entries that are farther away from the mean B. Data set (ii), because it has two entries that are far away from the mean. C. Data set (i), because it has more entries that are close to the mean. Which data set has the least sample standard deviation? A. Data set (i), because it has more entries that are close to the mean. B. Data set (ii), because it has less entries that are farther away from the mean. C. Data set (iii), because it has more entries that are farther away from the mean. (b) How are the data sets the same? How do they differ? A. The three data sets have the same standard deviations but have different means. B. The three data sets have the same mean, median and mode but have different standard deviation. C. The three data sets have the same mean and mode but have different medians and standard deviations. D. The three data sets have the same mode but have different standard deviations and means 13. Decide which method of data collection you would use to collect data for the study. A study of the effect on the human digestive system of a popular soda made with a caffeine substitute. Choose the correct answer below. A. Observational Study B. Simulation C. Survey D. Experiment 14. Use the given frequency distribution to find the: o (a) Class width o (b) Class midpoint of the first class o (c) Class boundaries of the first class

A. (a) 4 (b) 137.5 (c) 134.5-139.5 B. (a) 5 (b) 137 (c) 135-139 C. (a) 5 (b) 137 (c) 134.5-139.5 D. (a) 4 (b) 137.5 (c) 135-139 15. Consider the following sample data values. 5 14 15 21 16 13 9 19 (a) Calculate the range (b) Calculate the variance (c) Calculate the standard deviation a. The range is. (Type an integer or a decimal) b. The sample variance is. (Type an integer or decimal rounded to two decimal places as needed) c. The sample standard deviation is. (Type an integer or decimal rounded to two decimal places as needed) 16. Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (the pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below.

Find the regression equation. ^ Y = x + () (Round to three decimal places as needed) Choose the correct graph below.

(a) Predict the value of y for x = 4. Choose the correct answer below. 61. 1 62. 8 63. 8 64. Not meaningful o (b) Predict the value of y for x = 4.5. Choose the correct answer below. 61. 1 62. 8 63. 0 64. Not meaningful (c) Predict the value of y for x = 12. Choose the correct answer below. 57. 8 58. 1 59. 0 60. Not meaningful (d) Predict the value of y for x = 2.5. Choose the correct answer below. A. 57.8 B. 47.8 C. 111.0 D. Not meaningful 1.Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 20 students. The scores are given below. 27 15 39 43 23 14 49 33 57 35 36 14 13 38 22 24 22 48 14 23 2. Suppose that a study based on a sample from a targeted population shows that people at a pizza restaurant are hungrier than people at a coffee shop. A) make an inference based on the results of this study. B) what might this inference incorrectly imply? 3.Decide which method of data collecting you would use to collect data for the study below: A study of how fast a virus would spread in a school of fish. 4. Identify the sampling technique used: The name of 50 contestants are written on 50 cards. The cards are placed in a bag, and three names are picked from the bag. 5.In a poll of 1002 women in a country were asked whether they favor or oppose of the use of federal tax dollars to fund medical research using stem cells obtained from embryos. Among the women, 48% said they were in favor. 6. Identify the data set’s level of measurement. The years the summer Olympics were held in a particular country 7.Use the frequency histogram to answer each question. A) determine the # of classes B) estimate the frequency of the class with the least frequency. C) estimate the frequency of the class with the greatest frequency. D) determine the class width. 8.The data represents the time, in minutes, spent reading a political blog in a day. Construct a frequency distribution using 5 classes. In the table, include midpoints, relative frequencies, and cumulative frequencies. Which class had the greatest and least frequency? 9. Given a data set, how do you know whether to calculate σ or s? 10.Compare the three data sets on the right.

11.Use the given minimum and maximum data entries and the number of classes to find class width, lower class limits, and upper class limits. min = 9, max = 83, classes = 6 12.Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The table below shows the heights (in feet) and the number of stories of six notable buildings in a city. 13.For the following data (a) display the data in a scatter plat, (b) calculate the correlation coefficient r, and (c) make a conclusion about the type of correlation. The ages (in years) of 6 children and the number of words in their vocabulary. Age, X 1 2 3 4 5 6 Vocabulary Size 350 950 1200 1700 2250 2600 14.Determine whether the underlined numerical value is a parameter or a statistic. In a poll of a sample of 12,000 adults, in a certain city, 12% said they left for work before 6am. 15.Both data sets have a mean of 225. One has a SD of 16 and the other has an SD of 24. 16.Use the Venn diagram to identify the population and the sample.

17.Determine whether the variable is qualitative or quantitative. Breed of cat. 18.Use the relative frequency histogram below to complete each part. A) identify the class with the greatest and the class with the least frequency. B) approximate the greatest and least relative frequencies. C) approximate the relative frequency of the second class. 19.Use the given frequency distribution to find the: A) class width B) class midpoint of the first class C) class boundaries of the first class. Height (in inches) Class Frequency 50-52 5 53-55 8 56-58 12 59-61 13 62-64 11

20.For the following data (a) display the data in a scatter plot, (b) calculate the correlation coefficient r, and (c) make a conclusion about that type of correlation. The number of hours 6 students watched television during the weekend and the scores of each student who took a test the following monday. Hours spent Watching TV 0 1 2 3 3 5 Test Score 98 89 86 70 81 66 21.Explain the relationship below between variance and standard deviation. Can either of these measures be negative? 22.Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 30 students. The scores are shown below. 44 50 10 91 77 35 64 36 43 72 54 62 35 75 50 72 36 29 39 61 49 63 35 41 21 36 50 47 86 13 To find the 10% trimmed mean of a data set, order the data, delete the lowest and highest 10% of the entries 23.Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (the pair of variables have a significant correlation.) then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below. 24. Determine whether the underlined numerical value is a parameter or a statistic. Explain your reasoning. the average grade on the midterm exam in a certain math class of 50 students was an 88. 25.Suppose that a study based on a sample from a targeted population shows that people who own a fax machine have more money than people who do not. A) Make an inference based on the results of this study. B) What might this inference incorrectly imply? 26. Identify the data set’s level of measurement. The average daily temperatures (in degrees Fahrenheit) on five randomly selected days. 23, 33, 28, 34, 35 27.Identify the sampling technique used. The name of 100 contestants are written on 100 cards. The cards are placed in a bag, and three names are picked from the bag. 28.Which method of data collection should be used to collect data for the following study. The average weight of 175 students in a high school.

MATH 221 Quiz Week 5 ALL Answers are 100% Correct 3 Sets

These quizzes include formulas in Excel and in Word that can be used if numeric data is different from the one listed below 1. 1. Sixty percent of households say they would feel secure if they had $50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had $50,000 in savings. Find the probability that the number that say they would feel secure is (a) exactly five, (b) more than five, and (c) at most five. (a) Find the probability that the number that say they would feel secure is exactly five P(5) = (Round to three decimal places as needed) (b) Find the probability that the number that say they would feel secure is more than five. P(x>5) = (Round to three decimal places as needed) (c) Find the probability that the number that say they would feel secure is at most five. P(x≤5) = (Round to three decimal places as needed) 2. Suppose 80% of kids who visit a doctor have a fever, and 25% of kids with a fever have sore throats. What’s the probability that a kid who goes to the doctor has a fever and a sore throat? The probability is. (Round to three decimal places as needed) 3. Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n = 90, p = 0.8 The mean, µ is (Round to the nearest tenth as needed) The variance, σ2, is (Round to the nearest tenth as needed) The standard deviation, σ is (Round to the nearest tenth as needed) 4. Use the bar graph below, which shows the highest level of education received by employees of a company, to find the probability that the highest level of education for an employee chosen at random is E. The probability that the highest level of education for an employee chosen at random is E is. (Round to the nearest thousandth as needed) 5. A company that makes cartons finds that the probability of producing a carton with a puncture is 0.05, the probability that a carton has a smashed corner is 0.09, and the probability that a carton has a puncture and has a smashed corner is 0.005. Answer parts (a) and (b) below. o Are the events “selecting a carton with a puncture” and “selecting a carton with a smashed corner” mutually exclusive? o A. No, a carton can have a puncture and a smashed corner. 3. Yes, a carton can have a puncture and a smashed corner 4. Yes, a carton cannot have a puncture and a smashed corner 5. Mo, a carton cannot have a puncture and a smashed corner o If a quality inspector randomly selects a carton, find the probability that the carton has a puncture or has a smashed corner. The probability that a carton has a puncture or a smashed corner is 0.135. (Type an integer or a decimal. Do not round) 6. Given that x has a Poisson distribution with µ = 8, what is the probability that x = 3?

P(3) ≈ (Round to four decimal places as needed) 7. Perform the indicated calculation. = (Round to four decimal places as needed) 8. A frequency distribution is shown below. Complete parts (a) through (d) The number of televisions per household in a small town Televisions 0 1 2 3 Households 26 448 730 1400 a. Use the frequency distribution to construct a probability distribution X P(x) 0 1 2 3 (Round to the nearest thousandth as needed) b. Graph the probability distribution using a histogram. Choose the correct graph of the distribution below. Describe the histogram’s shape. Choose the correct answer below. A. Skewed right B. Skewed left C. Symmetric c. Find the mean of the probability distribution µ = (round to the nearest tenth as needed) Find the variance of the probability distribution σ2 = (round to the nearest tenth as needed) Find the standard deviation of the probability distribution σ = (round to the nearest tenth as needed) Interpret the results in the context of the real-life situation. d. The mean is 2.3, so the average household has about 3 television. The standard deviation is 0.6 of the households differ from the mean by no more that about 1 television A. The mean is 0.6, so the average household has about 1 television. The standard deviation is 0.8 of the households differ from the mean by no more that about 1 television B. The mean is 2.3, so the average household has about 2 television. The standard deviation is 0.8 of the households differ from the mean by no more that about 1 television C. The mean is 0.6, so the average household has about 1 television. The standard deviation is 2.3 of the households differ from the mean by no more that about 3 television 9. In the general population, one woman in eight will develop breast cancer. Research has shown that 1 woman is 650 carries a mutation of the BRCA gene. Nine out of 10 women with this mutation develop breast cancer. a. Find the probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene. The probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene is. (Round to one decimal place as needed) b. Find the probability that a randomly selected woman will carry the mutation of the BRCA gene and will develop breast cancer. The probability that a randomly selected woman will carry the gene nutation and develop breast cancer is. (Round to four decimal places as needed) c. Are the events of carrying this mutation and developing breast cancer independent or dependent? A. Dependent B. Independent 10. Students in a class take a quiz with eight questions. The number x of questions answered correctly can be approximated by the following probability distribution. Complete parts (a) through (e) X 0 1 2 3 4 5 6 7 8 P(x) 0.04 0.04 0.06 0.06 0.12 0.24 0.23 0.14 0.07 a. Use the probability distribution to find the mean of the probability distribution µ= (Round to the nearest tenth as needed) b. Use the probability distribution to find the variance of the probability distribution σ2= (Round to the nearest tenth as needed) c. Use the probability distribution to find the standard deviation of the probability distribution 2.0 (Round to the nearest tenth as needed) d. Use the probability distribution to find the expected value of the probability distribution 4.9 (Round to the nearest tenth as needed) e. Interpret the results A. The expected number of questions answered correctly is 2.0 with a standard deviation of 4.9 questions. B. The expected number of questions answered correctly is 4 with a standard deviation of 2.0 questions. C. The expected number of questions answered correctly is 4.9 with a standard deviation of 0.04 questions. D. The expected number of questions answered correctly is 4.9 with a standard deviation of 2.0 questions. 11. Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Randomly choosing a multiple of 5 between 21 and 49 The sample space is (Use a comma to separate answers as needed. Use ascending order) There are outcome(s) in the sample space. 12. Decide if the events shown in the Venn diagram are mutually exclusive.

Are the events mutually exclusive? A. Yes B. No 13. Determine whether the random variable is discrete or continuous. a. The number of free-throw attempts before the first shot is made b. The weight of a T-bone steak c. The number of bald eagles in the country d. The number of points scored during a basketball game e. The number of hits to a website in a day (a) Is the number of free-throw attempts before the first shot is made discrete or continuous? A. The random variable is continuous B, The random variable is discrete (b) Is the weight of a T-bone steak discrete or continuous? A. The random variable is discrete B. The random variable is continuous (c) Is the number of bald eagles in the country discrete or continuous? A. The random variable is discrete B. The random variable is continuous (d) Is the number of points scored during a basketball game discrete or continuous? A. The random variable is discrete B. The random variable is continuous (e) Is the number of hits to a website in a day discrete or continuous? A. The random variable is discrete B. The random variable is continuous 14. A survey asks 1100 workers: Has the economy forced you to reduce the amount of vacation you plan to take this year?” Fifty-six percent of those surveyed say they are reducing the amount of vacation. Twenty workers participating in the survey are randomly selected. The random variable represents the number of workers who are reducing the amount of vacation. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. Is the experiment a binomial experiment? A. Yes B. No What is a success in this experiment? A. Selecting a worker who is reducing the amount of vacation B. Selecting a worker who is not reducing the amount of vacation C. This is not a binomial experiment Specify the value of n. Select the correct choice and fill in any answer boxes in your choice A. N= B. This is not a binomial experiment Specify the value of p. Select the correct choice below and fill in any answer boxes in your choice. A. P= (Type an integer or a decimal) B. This is not a binomial experiment Specify the value of q. Select the correct choice below and fill in any answer boxes in your choice. A. Q= (Type an integer r a decimal) B. This is not a binomial experiment List the possible values of the random variable x A. X=0, 1, 2,…, 20 B. X=1, 2, 3,…, 1100 C. 1, 2,…, 20 D. This is not a binomial experiment 15. Determine whether the distribution is a discrete probability distribution. Is the distribution a discrete probability distribution? Why? Choose the correct answer below. A. Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive B. No, because the total probability is not equal to 1 C. Yes, because the distribution is symmetric D. No, because some of the probabilities have values greater than 1 or less than 0 16. The table below shows the results of a survey that asked 2872 people whether they are involved in any type of charity work. A person is selected at random from the sample. Complete parts (a) through (e). Frequency Occasionally Not at all Total Male 226 455 793 1474 Female 206 450 742 1398 Total 432 905 1535 2872 a. Find the probability that the person is frequently or occasionally involved in charity work P(being frequently involved or being occasionally involved) = (Round to the nearest thousandth as needed) b. Find the probability that the person is male or frequently involved in charity work P(being male or being frequently involved) = c. Find the probability that the person is female or not involved in charity work at all P(being female or not being involved) = 0.763 (Round to the nearest thousandth as needed) d. Find the probability that the person is female or not frequently involved in charity work P(being female or not being frequently involved) = (Round to the nearest thousandth as needed) e. Are the events “being female” and “being frequently involved in charity work” mutually exclusive? A. No, because 206 females are frequently involved in charity work. B. Yes, because no females are frequently involved in charity work. C. Yes, because 206 females are frequently involved in charity work. D. No, because no females are frequently involved in charity work. 17. For the given pair of events, classify the two events as independent or dependent. Swimming all day at the beach Getting a sunburn Choose the correct answer below. A. The two events are independent because the occurrence on one does not affect the probability of the occurrence of the other. B. The two events are dependent because the occurrence of one does not affect the probability of the occurrence of the other. C. The two events are independent because the occurrence of one affects the probability of the occurrence of the other. D. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other. 18. Outside a home, there is a 9-key keypad with letters A, B, C, D, E, F, G, H, and I that can be used to open the garage if the correct nine-letter code is entered. Each key may be used only once. How many codes are possible? The number of possible codes is. 19. Determine the number of outcomes in the event. Decide whether the event is a simple event or not. A computer is used to select randomly a number between 1 and 9, inclusive. Event C is selecting a number less than 5. Event has outcome(s) Is the event a simple event? 1.Decide whether the random variable x is discrete or continuous X represents the number of home theater systems sold per month at an electronics store. 1.Evaluate the given expression and express the results using the usual format for writing numbers (instead of scientific notation 36C2 2.Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. N = 80, p = 0.4 2.Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. N = 128, p = 0.36 3. A new phone answering system for a company is capable of handling four calls every 10 minutes. Prior to installing the new system, company analysts determined that the incoming calls to the system are Poisson distributed with a mean equal to one every 10 minutes. If this incoming call distribution is what the analysts think it is, what is the probability that in a 10 – minute period more calls will arrive than the system can handle? 3.Suppose 90% of kids who visit a doctor have a fever, and 35% of kids with a fever have sore throats. What’s the probability that a kid who goes to the doctor has a fever and a sore throat? 4. You randomly select one card from a standard deck. Event A is selecting a nine. Determine the number of outcomes in event A. then decide whether the event is a simple event or not. 4.A frequency distribution is shown below. Complete parts (a) through €. The number of dogs per household in a small town. Dogs 0 1 2 3 4 5 Households 1295 416 163 47 27 12 5.22% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the number of students who say they use credit cards because of the rewards program is (a) exactly two, (b) more than two, and (c) between two and five inclusive. If convenient, use technology to find the probabilities. 5.The table below shows the results of a survey that asked 2870 people whether they are involved in any type of charity work. A person is selected at random from the sample. Complete parts (a) through (e). 6.The table below shows the results of a survey that asked 2885 people whether they are involved in any type of charity work. A person is selected at random from the sample. Complete parts (a) through (e). 6.Identify the sample space of the probability experiment and determine the number of outcomes in a sample space. Randomly choosing an even number between 10 and 20, inclusive. 7.Students in a class take a math quiz with eight questions. The number x of questions answered correctly can be approximated by the following probability distributions. Complete parts (a) through € 7.Determine whether the events E and F are independent or dependent. Justify your answer. 8.A certain lottery has 29 numbers. In how many different ways can 4 of the numbers be selected? (assume that order of selection is not important.) 8.Determine the required value of the missing probability to make the distribution a discrete probability distribution 9.Determine whether the distribution Is a discrete probability distribution. 9.The histogram shows the distribution of stops for red traffic lights a commuter must pass through on her way to work. Use the histogram to find the mean, variance, standard deviation, and expected value of the probability distribution. 10.Decide if the events are mutually exclusive. Event A: Randomly selecting someone who is married Event B: Randomly selecting someone who is a bachelor 10.A standard deck of cards contains 52 cards. One card is selected from the deck. A) compute the probability of randomly selecting a six or three. B) compute the probability of randomly selecting a six, three, or king. C) compute the probability of randomly selecting an eight or club. 11.A survey asks 1200 workers, “has the economy forced you to reduce the amount of vacation you plan to take this year?” 52% of those surveyed say they are reducing the amount of vacation. Ten workers participating in the survey are randomly selected. The random variable represents the number of workers who are reducing the amount of vacation. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p and q. 11.A study found that 36% of the assisted reproductive technology (ART) cycles resulted in pregnancies. Twenty eight percent of the ART pregnancies resulted in multiple births. 12.Use the bar graph below, which shows the highest level of education received by employees of a company, to find the probability that the highest level of education for an employee chosen random is E. 12.A golf-course architect has four linden trees, five white birch trees, and two bald cypress tress in a row along a fairway. In how many ways can the landscaper plant the trees in a row, assuming that the trees are evenly spaced? 13.Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. 13.Decide if the events are mutually exclusive. Event A) Receiving a phone call from someone who opposes all cloning Event B) Receiving a phone call from someone who approves of cloning sheep. 14.Determine whether the events E and F are independent or dependent. Justify your answer. 14.47% of men consider themselves a professional baseball fan. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Find the probability tha the number who consider themselves baseball fans is (a) 8, (b) at least 8, and (c) less than eight. If convenient, use technology to find the probabilities. 15.Suppose 60% of kids who visit a doctor have a fever, and 30% of kids with a fever have sore throats. What’s the probability that a kid who goes to the doctor has a fever and a sore throat? 15.Given that x has a Poisson distribution with ᶙ = 8, what is the probability that x = 1? 16.Perform the indicated calculation. 16.Use the frequency distribution, which shows the responses of a survey of college students when asked, “how often do you wear a seat belt when riding a car driven by someone else?” find the following probabilities of responses of college students from the survey chosen at random. 17.A frequency distribution is shown below. Complete parts (a) through (d). The number of televisions per household in a small town. Televisions 0 1 2 3 Households 2 443 723 1409 17.About 30% of babies born with a certain ailment recover fully. A hospital is caring for six babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. 18.A study found that 37% of the assisted reproductive technology (ART) cycles resulted in pregnancies. 24% of the ART pregnancies resulted in multiple births. A) find the probability that a random selected ART cycle resulted in a pregnancy and produced a multiple birth. B) find the probability that a randomly selected ART cycle that resulted in a pregnancy did not produce a multiple birth. C) would it be unusual for a randomly selected ART cycle to result in a pregnancy and produce a multiple birth? 18. You randomly select one card from a standard deck. Event A is selecting a three. Determine the number of outcomes in event A. then decide whether the event is a simple event or not. 19.A company that makes cartons finds the probability of producing a carton with a puncture is 0.07, the probability that a carton has a smashed corner is 0.1, and the probability that a carton has a puncture and has a smashed corner is 0.007. answer parts (a) and (b) 19.Determine whether the random variable is discrete or continuous. a. the # of bald eagles in the country. b. the weight of a t-bone steak. c. the time it takes for a light bulb to burn out. d. the number of fish caught during a fishing tournament. e. the distance a baseball travels in the air after being hit. MATH 221 Quiz Week 7 with All Formulas ALL Answers are 100% Correct 4 Sets

These quizzes include formulas in Excel and in Word that can be used if numeric data is different from the one listed below 1. These quizzes include formulas in Excel and in Word that can be used if numeric data is different from the one listed below. 1. A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 35,000 miles and a standard deviation of 2800 miles. He wants to give a guarantee for free replacement of tires that don’t wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires? Tires that wear out by …miles will be replaced free of charge. 2. Find the indicated z-score shown in the graph to the right.

The z-score is 3. A researcher wishes to estimate, with 95% confidence, the amount of adults who have high-speed internet access. Her estimate must be accurate within 4% of the true proportion. a) find the minimum sample size needed, using a prior study that found that 32% of the respondents said they have high-speed internet access(b) no preliminary estimate is available. Find the minimum sample size needed.a) = b) = 4. The total cholesterol levels of a sample of men aged 35-44 are normally distributed with a mean of 221 milligrams per deciliter and a standard deviation of 37.7 milligrams per deciliter. (a) what percent of men have a total cholesterol level less than 228 milligrams per deciliter of blood? (b) if 251 men in the 35-44 age group are randomly selected, about how many would you expect to have a total cholesterol level greater than 264 milligrams per deciliter of blood? a) = b) = 5. Find the z-score that has a 12.1% of the distribution’s area to it’s left. Answer = 6. A doctor wants to estimate the HDL cholesterol of all 20-29 year old females. How many subjects are needed to estimate the HDL cholesterol within 2 points with 99% confidence assuming σ = 18.1? suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size required? 99% = 90% = how does the decrease in confidence affect the sample size required? Answer: 7. Use a table of cumulative areas under the normal curve to find the z-score that corresponds to the given cumulative area. If the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the z-score halfway between the corresponding z-scores. If convenient, use technology to find the z-score. 0.054 Answer: 8. In a survey of 3076 adults, 1492 say they have started paying bills online in the last year. Construct a 99% confidence interval for the population proportion. Interpret the results. Answer: With 99% confidence, it can be said that the… 9. Assume the random variable x is normally distributed with mean u = 89 and standard deviation o = 4. Find the indicated probability. P(7639) 12. The systolic blood pressures of a sample of adults are normally distributed, with a mean pressure of 115 millimeters of mercury and a standard deviation of 3.6 millimeters of mercury. The systolic blood pressures of four adults selected at random are 119 millimeters of mercury, 113 millimeters of mercury, and 127 millimeters of mercury. The graph of the standard normal distribution is shown to the right. Complete parts (a) through (c) below. o Without converting to z-scores, match the values with the letters A, B, V, and D on the given graph above of the standard normal distribution. o Find the z-score that corresponds to each value and check your answers to part (a) o Determine whether any of the values are unusual, and classify them as either unusual or very unusual. Select the correct answer below and, if necessary, fill in the answer box(es) within your choice…. 13. Use a table of cumulative areas under the normal curve to find the z-score that corresponds to the given cumulative area. If the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the z-score halfway between corresponding z-scores. If convenient, use technology to find the z-score. 0.049. 14. Find the critical value t for the confidence level c =0.99 and sample size n = 13. Click the icon to view the t-distribution table. 13. Find the margin of terror for the given values of c,s, and n. C = 0.95, S = 3.9, N = 26 14 For the standard normal distribution shown on the right, find the probability of z occurring in the indicated region. -0.62 Answer = 14. You are given the sample mean and sample and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals. A random sample of 36 gas grills has a mean price of $637.60 and a standard deviation of $55.80 14.Use the central limit theorem to find the mean and the standard error of the mean of the indicated sampling distribution. The sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 113 pounds and a standard deviation of 39.1 pounds. Random samples of size 18 are drawn from this population and the mean of each sample is determined. 15. What requirements are necessary for a normal probability distribution to be a standard normal probability distribution? 15.Find the indicated probability using the standard normal distribution. P (-0.21 35) Answer = 21.In a survey of 3068 adults, 1462 say they have started paying bills online in the last year. Construct a 99% confidence interval for the population proportion. Interpret the results. Choose the correct answer below… 22. Use a table of cumulative areas under the normal curve to find the z-score that corresponds to the given cumulative area. If the area is not in the table, use the try closest to the area. If the area is halfway between two entries, use the z-score halfway between the corresponding z-scores. If convenient, use technology to find the z-score. 0.051. Answer = 22. In a survey of 640 male ages 18-64, 392 say they have gone to the dentist in the past year. Construct a 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the confidence intervals. If convenient, use technology to construct the confidence intervals. The 90% confidence interval is 0.580, 0.644 The 95% confidence interval is 0.575, 0650 With the given confidence, it can be said that the population proportion of males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval. 22. Find the critical value Tc for the confidence level c = 0.80 and sample size n = 14. Tc = 1.350 23. Assume the random variable x is normally distributed with mean u = 50 and standard deviation = 7. P ( X > 38) 23. For the standard normal distribution shown on the right, find the probability in the indicated region. 23.The total cholesterol levels of a sample of men aged 35-44 are normally distributed with a mean of 206 milligrams per deciliter and a standard deviation of 37.6 milligrams per deciliter. A) what % of the men have a total cholesterol level less than 240 milligrams per deciliter of blood? B) if 240 men in the 35-44 age group are randomly selected, about how many would you expect to have total cholesterol level greater than 252 milligrams per deciliter of blood? MATH 221 Homework Week 1

1 Determine whether the data set is a population or a sample. Explain your reasoning. The age of each resident in an apartment building. 1 Determine whether the data set is a population or a sample. Explain your reasoning. The salary of each baseball player in a league 1. Determine whether the data set is a population or a sample. The number of restaurants in each city in a state. 2 Determine whether the underlined value is a parameter or a statistic. The average age of men who have walked on the moon was 39 years, 11 months, 15 days. Is the value a parameter or a statistic? 2 Determine whether the data set is a population or a sample. Explain your reasoning. The number of pets for 20 households in a town of 300 households. Choose the correct answer below. 2. Determine whether the data is a population or sample. The age of one person per row in a cinema. 3 Determine whether the given value is a statistic or a parameter. In a study of all 3336 professors at a college, it is found that 55% own a vehicle. 3 Determine whether the underlined value is a parameter or a statistic. In a national survey of high school students (grades 9-12), 25% or respondents reported that someone had offered, sold, or given them an illegal drug on school property. 3. Determine whether the underlined value is a parameter or a statistic. The average age of men who have walked on the moon was 39 years, 11 months, 15 days. 4 Determine whether the given value is a statistic or a parameter. In a study of all 4901 professors at a college, it is found that 35% own a television. 4 Determine whether the given value is a parameter or a statistic. In a study of all 1290 employees at a college, it is found that 40% own a computer. 4. Determine whether the given value is a statistic or a parameter. A sample of professors is selected and it is found that 65% own a television. 5 Determine whether the variable is qualitative or quantitative. Favorite film Is the variable qualitative or quantitative? 5 Determine whether the given value is a statistic or a parameter. A sample of employees is selected and it is found that 45% own a vehicle. 5. Determine whether the given value is a statistic or a parameter. A sample of seniors is selected and it is found that 65% own a computer. 6 Determine whether the variable is qualitative or quantitative. Hair color Is the variable qualitative or quantitative? 6 Determine whether the variable is qualitative or quantitative. Favorite sport Is the variable qualitative or quantitative? 6. Determine whether the variable is qualitative or quantitative Favorite Film 7 The regions of a country with the six highest per capital incomes last year are shown below. 1. Southeast Western 3 Eastern 4 Northeast 5 Southeast 6 Northern Determine whether the data are qualitative or quantitative and identify the data set’s level of measurement. What is the data set’s level of measurement? 1. Ratio B. Ordinal C. Interval D. Nominal 7 Determine whether the variable is qualitative or quantitative. Car license Is the variable Quantitative? 7.Determine whether the variable is qualitative or quantitative Gallons of water in a swimming pool 8 Which method of data collection should be used to collect data for the following study. The average age of the 105 residents of a retirement community. 8 The region representing the top salesperson is a corporation for the past six years is shown below. Northern Northern Eastern Southeast Eastern Northern Determine whether the data are qualitative or quantitative and identify the data set’s level of measurement. Are the data qualitative or quantitative? What is the data set’s level of measurement? 8. The region of a country with the longest life expectancy for the past six years is shown below. Western, Southeast, Southwest, Northeast, Northeast, Southeast, 9 Decide which method of data collection you would use to collect data for the study. A study of the effect on the taste of a popular soda made with a caffeine substitute. 9 Which method of data collection should be used to collect data for the following study. The average weight of 188 students in a high school. 9. Which method of data collection should be used to collect data for the following study. The average age of 124 residents of a retirement community 10 Microsoft wants to administer a satisfaction survey to its customers. Using their customer database, the company randomly selects 60 customers and asks them about their level of satisfaction with the company. What type of sampling is used? 10 Decide which method of data collection you would use to collect data for the study. A study of the effect on the human digestive system of a snack food made with a sugar substitute. 10. Decide which method of data collection you would use to collect data for the study. A study of the effect on human digestive system of a snack food made with a fat substitute. 11 A newspaper asks its readers to call in their opinion regarding the number of books they have read this month. What type sampling is used? 11 General Motors wants to administer a satisfaction survey to its current customers. Using their customer database, the company randomly selects 80 customers and asks them about their level of satisfaction with the company. What type of sampling is used? 12 Determine whether you would take a census or a sampling to collect data for the study described below. The most popular chain restaurant among the 60,000 employees of a company. Would you take a census or use a sampling? 11. Sony wants to administer a satisfaction survey to its current customers. Using their customer database, the company randomly selects 50 customers and asks them about what their level of satisfaction with the company. 12 A magazine asks its readers to call in their opinion regarding the quality of the articles. What type of sampling is used? 12. A television station asks its viewers to call in their opinion regarding the desirability of programs in high definition TV. 13 Math the plot with a possible description of the sample.

Choose the correct answer below. 1. Top speeds (in miles per hour) of a sample of sports cars 2. Time (in minutes) it takes a sample of employees to drive to work 3. Grade point averages of a sample of students with finance majors 4. Ages (in years) of a sample of residents of a retirement home 13 Determine whether you would take a census or use a sampling to collect data for the study described below. The most popular house color among the 40,000 employees of a company. Would you take a census or use a sampling? 13. Determine whether you would take a census or use a sampling to collect data for the study described below. The most popular chain restaurant among the 35 employees of a company. 14 Use a stem-and-leaf plot to display the data. The data represent the heights of eruptions by geyser. What can you conclude about the data? 108 90 110 150 140 120 100 130 110 100 118 106 98 102 105 120 111 130 96 124 Choose the correct stem-and-leaf plot. (Key: 15 ǀ 5 = 155)

What can you conclude about the data? 14 Match the plot with a possible description of the sample. Choose the correct answer below. 1. Fastest serve (in miles per hour) of a sample of top tennis players 2. Grade point averages of a sample of students with finance major 3. Time (in minutes) it takes a sample of employees to drive to work 4. Ages (in years) of a sample of residents of a retirement home 14.Match the plot with a possible description of the sample. 15 Determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these.

Choose the best answer below. 1. Skewed right 2. Skewed left 3. Symmetric 4. Uniform 5. None of these 15 Use a stem-and-leaf plot to display the data. The data represent the heights of eruptions by a geyser. What can you conclude about the data? 106 90 110 150 140 120 100 130 110 101 115 100 99 107 103 120 115 130 95 121 What can you conclude about the data?

16 The maximum number of seats in a sample of 13 sport utility vehicles are listed below. Find the mean, median, and mode of the data. 5 7 8 8 5 6 4 4 4 4 4 4 5 Find the mean. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 1. The mean is (Type the integer or decimal rounded to the nearest tenth as needed) 1. The data does not have a mean. Find the median. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 1. The median is (Type the integer or decimal rounded to the nearest tenth as needed) 1. The data does not have a median. Find the mode. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 1. The median is (Type the integer or decimal rounded to the nearest tenth as needed) 1. The data does not have a mode. 16 Determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of those. Choose the best answer below. 1. Skewed right 2. Skewed left 3. Symmetric 4. Uniform 5. None of these 6. Determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these. 17 Find the range, mean, variance, and standard deviation of the sample data set. 14 12 13 8 20 7 18 16 15 The range is 17 The maximum number of seats in a sample of 13 sport utility vehicles are listed below. Find the mean, median, and mode of the data. 8 10 11 11 8 7 7 7 9 7 7 7 8 Find the mean. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 1. The mean is (Type the integer or decimal rounded to the nearest tenth as needed) 1. The data does not have a mean. Find the median. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 1. The median is (Type the integer or decimal rounded to the nearest tenth as needed) 1. The data does not have a median Find the mode. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 1. The mode is (Type the integer or decimal rounded to the nearest tenth as needed) 1. The data does not have a mode 2. The maximum # of seats in a sample of 13 sport utility vehicles are listed below. Find the mean, median, and mode of the data. 8 8 11 11 8 7 7 7 9 7 7 7 10 Find the mean. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 18 The ages of 10 brides at their first marriage are given below. 35.9 32.6 28.7 37.7 44.7 31.3 29.5 23.2 22.4 33.6 (a) Find the range of the data set. Range = (round to the nearest tenth as needed) (b) Change 44.7 to 61.3 and find the range of the new data set. Range = 38.9 (round to the nearest tenth as needed) (c) Compare your answer to part (a) with your answer to part (b) 1. Changing the maximum value of the data set does not affect the range 2. Changing the minimum value of the data set does not affect the range 3. Changing the minimum value of the data set greatly affects the range 4. Changing the maximum value of the data set greatly affects the range 18 Find the range, mean, variance, and standard deviation of the sample data set. 10 14 13 5 19 11 18 12 9 The range is 18. Find the range, mean, variance, and standard deviation of the sample data set. 8 15 14 17 9 7 13 11 20 19 Heights of men on a baseball team have a bell-shaped distribution with a mean of 185 cm and a standard deviation of 6 cm. Using the empirical rule, what is the approximate percentage of the men between the following values? 1. 173 cm and 197 cm 2. 167 cm and 203 cm A % of the men are between 173 cm and 197 cm B % of the men are between 167 cm and 203 cm (Do not round) 19.The ages of 10 brides at their first marriage are given below. 24.4 31.8 35.8 32.5 44.2 24.5 26.2 24.6 22.5 27.2 20 The mean value of land and buildings per acre from a sample of farms is $1400, with a standard deviation of $100. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 70. 1500. Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1300 and $1500. farms (Round to the nearest whole number as needed) 1. If 28 additional farms were sampled, about how many of these additional farms would you expect to have land and building value between $1300 per acre and $1500 per acre? 2. Heights of men on a baseball team have a bell-shaped distribution with a mean of 182 cm and a standard deviation of 6 cm. Using the empirical rule, what is the approximate percentage of the men between the following values? A. 170 cm and 194 cm B. 176 cm and 188 cm 21 Use the box-and-whisker plot to identify (a) The minimum entry (b) The maximum entry (c) The first quartile (d) The second quartile (e) The third quartile (f) The interquartile range (a) Min = (b) Max = (c) Q 1 = (d) Q 2 = (e) Q 3 = (f) IQR = 19 The ages of 10 brides at their first marriage are given below 22.6 23.7 35.6 39.2 44.7 29.6 30.8 31.7 24.5 28.2 (a) Find the range of the data set Range = (b) Change 44.7 to 68.3 and find the range of the new data set Range = (c) Compare your answer to part (a) with your answer to part (b). 1. Changing the maximum value of the data set greatly affects the range 2. Changing the minimum value of the data set greatly affects the range 3. Changing the maximum value of the data set does not affect the range 4. Changing the minimum value of the data set does not affect the range 20 Heights of men on a baseball team have a bell-shaped distribution with a mean of 172 cm and a standard deviation of 7 cm. Using the empirical rule, what is the approximate percentage of the men between the following values? 1. 151 cm and 193 cm 2. 165 cm and 179 cm 3. % of the men are between 151 cm and 193 cm (Do not round) 4. % of the men are between 165 cm and 179 cm (Do not round) 20 The midpoints A, B, and C are marked on the histogram. Match them to the indicated scores. Which scores, if any, would be considered unusual? The point A corresponds with z = The point B corresponds with z = The point C corresponds with z = Which scores, if any, would be considered unusual? 1. 41 2. -2.17 3. 0 4. None MATH 221 Homework Week 2

1. 1. Two variables have a positive linear correlation. Does the dependent variable increase or decrease as the independent variable increases? 2. Two variables have a positive linear correlation. Does the dependent variable increase or decrease as the independent variable increases? 3. Discuss the difference between r and p Choose the correct answers below. R represents the sample correlation coefficient. P represents the population correlation coefficient 2. Discuss the difference between r and p. 3. The scatter plot of a paired data set is shown. Determine whether there is a perfect positive linear correlation, a strong positive linear correlation, a perfect negative linear correlation, a strong negative linear correlation, or no linear correlation between the variables.

Choose the correct answer below. A. no linear correlation B. strong positive linear correlation C. strong negative linear correlation D. perfect negative linear correlation E. perfect positive linear correlation 3 The scatter plot of a paired data set is shown. Determine whether there is a perfect positive linear correlation, a strong positive linear correlation, a perfect negative linear correlation, a strong negative linear correlation, or no linear correlation between the variables.

3. The scatter plot of a paired data set is shown. Determine whether there is a perfect positive linear correlation, a strong positive linear correlation, a perfect negative linear correlation, a strong negative linear correlation, or no linear correlation between the variables. 4 Identify the explanatory variable and the response variable. A golfer wants to determine if the amount of practice every year can be used to predict the amount of improvement in his game. 4 Identify the explanatory variable and the response variable. A teacher wants to determine if the amount of textbook used by her students can be used to predict the students’ test scores 4.Identify the explanatory variable and the response variable. a golfer wants to determine if the amount of practice every year can be used to predict the amount of improvement in his game. 5 Two variables have a positive linear correlation. Is the slope of the regression line for the variables positive or negative? 5.Two variables have a positive linear correlation. Is the slope of the regression line for the variables positive or negative? 6 Given a set of data and a corresponding regression line, describe all values of x that provide meaningful predictions for y. 4. Prediction values are meaningful for all x-values that are realistic in the context of the original data set. 5. Prediction values are meaningful for all x-values that are not included in the original data set. 6. Prediction values are meaningful for all x-values in (or close to) the range of the original data. 5.Two variables have a positive linear correlation. Is the slope of the regression line for the variables positive or negative? 7 Match this description with a description below. The y-value of a data point corresponding to Choose the correct answer below.

8 Match this description with a description below. The y-value for a point on the regression line corresponding to Choose the correct answer below.

8. Match this description with a description below. the y-value of a data point corresponding to x 9 Match the description below with its symbol(s). The mean of the y-values Select the correct choice below.

10 Match the regression equation with the appropriate graph. Choose the correct answer below.

10 Match the regression equation with the appropriate graph.

11. Match the regression equation y = 1.662x + 83.34 with the appropriate graph. 12 Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? R= -0.312 Calculate the coefficient of determination What does this tell you about the explained variation of the data about the regression line? % of the variation can be explained by the regression line. About the unexplained variation? % of the variation is unexplained and is due to other factors or to sampling error. (Round to three decimal places as needed) 12 Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? R= -0.324 Calculate the coefficient of determination What does this tell you about the explained variation of the data about the regression line? % of the variation can be explained by the regression line. About the unexplained variation? % of the variation is unexplained and is due to other factors or to sampling error. 12 Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? R = 0.481 Calculate the coefficient of determination What does this tell you about the explained variation of the data about the regression line? % of the variation can be explained by the regression line. % of the variation is unexplained and is due to other factors or to sampling error. 12 Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? R = 0.224 Calculate the coefficient of determination What does this tell you about the explained variation of the data about the regression line? % of the variation can be explained by the regression line. % of the variation is unexplained and is due to other factors or to sampling error. 12 The equation used to predict college GPA (range 0-4.0) is is high school GPA (range 0-4.0) and x2 is college board score (range 200-800). Use the multiple regression equation to predict college GPA for a high school GPA of 3.5 and college board score of 400. The predicted college GOA for a high school GPA of 3.5 and college board of 400 is. (Round to the nearest tenth as needed). 12. Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? R = 0.862 13 Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? R = 0.909 Calculate the coefficient of determination What does this tell you about the explained variation of the data about the regression line? % of the variation can be explained by the regression line. % of the variation is unexplained and is due to other factors or to sampling error. (Round to three decimal places as needed) 13 The equation used to predict the total body weight (in pounds) of a female athlete at a certain school is the female athlete’s height (in inches) and x2 is the female athlete’s percent body fat. Use the multiple regression equation to predict the total body weight for a female athlete who is 64 inches tall and has 17% body fat. The predicted total body weight for a female athlete who is 64 inches tall and has 17% body fat is pounds. 13.Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the about the regression line? About the unexplained variation? R = 0.592 14 The equation used to predict college GPA (range 0-4.0) is high school GPA (range 0-4.0) and X2 is college board score (range 200-800). Use the multiple regression equation to predict college GPA for a high school GPA of 3.2 and a college board score of 500. The predicted college GPA for a high school GPA of 3.2 and college board score of 500 is. 14.The equation used to predict college GPA (range 0-4.0) is y = 0.21 + 0.52x + 0.002x, where x is high school GPA (range 0-4.0) and x is college board score (range 200-800). Use the multiple regression equation to predict college gpa for a high school gpa of 3.2 and a college board score of 600. 15 The equation used to predict the total body weight (in pounds) of a female athlete at a certain school is the female athlete’s height (in inches) and X2 is the female athlete’s percent body fat. Use the multiple regression equation to predict the total body weight for a female athlete who is 67 inches tall and has 24% body fat. The predicted total body weight for a female athlete who is 67 inches tall and has 24% body fat is pounds. 15.The equation used to predict the total body weight of a female athlete at a certain school is y = -112 + 3.29x + 1.64x, where x is the female athlete’s height and x is the females athlete’s % body fat. Use the multiple regression equation to predict the total body weight for a female athlete who is 63 inches tall and has 19% body fat. MATH 221 Homework Week 3

1 The access code for a car’s security system consist of four digits. The first digit cannot be zero and the last digit must be odd. How many different codes are available? 1 The access code for a car’s security system consist of four digits. The first digit cannot be 6 and the last digit must be even or zero. How many different codes are available? 1.The access code for a car’s security system consists of four digits. The first digit cannot be 1 and must e even or 0. How many different codes are there? 2 A probability experiment consists of rolling a 6-sided die. Find the probability of the event below: Rolling a number is less than 5 2 A probability experiment consists of rolling a 6-sided die. Find the probability of the event below: Rolling a number is less than 4 2. A probability experiment consists of rolling a 6-sided die. Find the probability of rolling a number less than 4. 3 Use the frequency distribution, which shows the responses of a survey of college students when asked, “How often do you wear a seat belt when riding in a car driven by someone else?” Find the following probabilities of responses of college students from the survey chosen at random.

Use the frequency distribution, which shows the responses of a survey of college students when asked, “how often do you wear a seat belt when riding in a car driven by someone else? Find the following probability of responses of college students from the survey chosen at random. 4 Determine whether the events E and F are independent or dependent. Justify your answer. 1. E: A person having an at-fault accident. F: The same person being prone to road rage. 1. E and F are dependent because having an at-fault accident has no effect on the probability of a person being prone to road rage. 2. E and F are dependent because being prone to road rage can affect the probability of a person having an at-fault accident. 3. E and F are independent because having an at-fault accident has no effect on the probability of a person being prone to road rage. 4. E and F are independent because being prone to road rage has no effect on the probability of a person having an at-fault accident. 5. E: A randomly selected person accidentally killing a spider. F: Another randomly selected person accidentally swallowing a spider. 1. E can affect the probability of F, even if the two people are randomly selected, so the events are dependent. 2. E can affect the probability of F because the people were randomly selected, so the events are dependent. 3. E cannot affect F and vice versa because the people were randomly selected, so the events are independent. 4. E cannot affect F because “person 1 accidentally killing a spider” could never occur, so the events are neither dependent nor independent. 5. E: The consumer demand for synthetic diamonds. F: The amount of research funding for diamond synthesis. 1. The consumer demand for synthetic diamonds could not affect the amount of research funding for diamond synthesis, so E and F are independent. 2. The consumer demand for synthetic diamonds could affect the amount of research funding for diamond synthesis, so E and F are dependent. 3. The amount of research funding for diamond synthesis could affect the consumer demand for synthetic diamonds, so E and F are dependent. 4. E: The unusually foggy weather in London on May 8 F: The number of car accidents in London on May 8 1. The unusually foggy weather in London on May 8 could not affect the number of car accidents in London on May 8, so E and F are independent. 2. The number of car accidents in London on May 8 could affect the unusually foggy weather in London on May 8, so E and F are dependent 3. The unusually foggy weather in London on May 8 could affect the number of car accidents in London on May 8, so E and F are dependent 4. Determine whether the events E and F are independent or dependent. Justify your answer. (a) E: A person having an at-fault accident F: The same person being prone to road rage (b) E: A randomly selected person accidentally killing a spider. F: Another random person swallowing a spider (c) E: The consumer demand for synthetic diamonds F: The amount of research funding for diamond synthesis 5 The table below shows the results of a survey in which 147 families were asked if they own a computer and if they will be taking a summer vacation this year. Summer Vacation This Year Yes No Total Own a Yes 46 11 57 Computer No 56 34 90 Total 102 45 147 a. Find the probability that a randomly selected family is not taking a summer vacation this year. The probability is (Round to the nearest thousandth as needed.) b. Find the probability that a randomly selected family owns a computer. The probability is (Round to the nearest thousandth as needed.) c. Find the probability that a randomly selected family is taking a summer vacation this year given that they own a computer. The probability is (Round to the nearest thousandth as needed.) d. Find the probability that a randomly selected family is taking a summer vacation this year and owns a computer. The probability is (Round to the nearest thousandth as needed.) e. Are the events of owning a computer and taking a summer vacation this year independent or dependent events? 6 The table below shows the results of a survey in which 147 families were asked if they own a computer and if they will be taking a summer vacation this year. Summer Vacation This Year Yes No Total Own a Yes 47 11 58 Computer No 56 33 89 Total 103 44 147 1. Find the probability that a randomly selected family is not taking a summer vacation this year. The probability is 1. Find the probability that a randomly selected family owns a computer. The probability is 1. Find the probability that a randomly selected family is taking a summer vacation this year given that they own a computer. The probability is 1. Find the probability that a randomly selected family is taking a summer vacation this year and owns a computer. The probability is (Round to the nearest thousandth as needed.) 1. Are the events of owning a computer and taking a summer vacation this year independent or dependent events? 2. The table below shows the results of a survey in which 146 families were asked if they own a computer and if they will be taking a summer vacation this year. (A) Find the probability that a random family is not taking a summer vacation this year. (B) Find the probability that a random family owns a computer (C) Find the probability that a random family is taking a vacation given that they own a computer (D) Find the probability that a random family is taking a vacation and own a computer. (E) Are the events of owning a computer and taking a vacation independent or dependent?6 The table below shows the results of a survey in which 147 families were asked if they own a computer and if they will be taking a summer vacation this year. Summer Vacation This Year Yes No Total Own a Yes 47 11 58 Computer No 56 33 89 Total 103 44 147 1. a. Find the probability that a randomly selected family is not taking a summer vacation this year. The probability is 2. Find the probability that a randomly selected family owns a computer. The probability is 3. Find the probability that a randomly selected family is taking a summer vacation this year given that they own a computer. The probability is 4. Find the probability that a randomly selected family is taking a summer vacation this year and owns a computer. The probability is 5. Are the events of owning a computer and taking a summer vacation this year independent or dependent events? 7 A distribution center receives shipments of a product from three different factories in the quantities of 50, 30, and 20. Three times a product is selected at random, each time without replacement. Find the probability that (a) all three products came from the second factory and (b) none of the three products came from the second factory. 7 A distribution center receives shipments of a product from three different factories in the quantities of 50, 30, and 20. Three times a product is selected at random, each time without replacement. Find the probability that (a) all three products came from the second factory and (b) none of the three products came from the second factory. 1. The probability that all three products came from the second factory is 2. The probability that none of the three products came from the second factory is a. The probability that all three products came from the second factory is (Round to the nearest thousandth as needed.) b. The probability that none of the three products came from the second factory is (Round to the nearest thousandth as needed.) 8 A standard deck of cards contains 52 cards. One card is selected from the deck. a. Compute the probability of randomly selecting a spade or heart b. Compute the probability of randomly selecting a spade or heart or diamond c. Compute the probability of randomly selecting a seven or club a. P(spade of heart)= (Type an integer or a simplified fraction.) b. P(spade or heart or diamond)= (Type an integer or a simplified fraction.) c. P(seven or club)= (Type an integer or a simplified fraction.) 8 A standard deck of cards contains 52 cards. One card is selected from the deck. a. Compute the probability of randomly selecting a three or eight b. Compute the probability of randomly selecting a three or eight of king c. Compute the probability of randomly selecting a queen or diamond a. P(spade of heart)= (Type an integer or a simplified fraction.) b. P(spade or heart or diamond)= (Type an integer or a simplified fraction.) c. P(seven or club)= (Type an integer or a simplified fraction.) 9 The percent distribution of live multiple-delivery births (three or more babies) in a particular year for a women 15 to 54 years old is shown in the pie chart. Find each probability.

10 The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random. Complete parts (a) through (d). Nursing majors Non-nursing majors Total Males 92 1019 1111 Females 700 1725 2425 Total 792 2744 3536 1. Find the probability that the student is male or a nursing major P (being male or being nursing major) = 1. Find the probability that the student is female or not a nursing major. P( being female or not a nursing major) = 1. Find the probability that the student is not female or a nursing major P(not being female or being a nursing major) = Are the events “being male” and “being a nursing major” mutually exclusive? 1. No, because there are 92 males majoring in nursing 2. No, because one can’t be male and a nursing major at the same time 3. Yes, because one can’t be male and a nursing major at the same time 4. Yes, because there are 97 males majoring in nursing 10 The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random. Complete parts (a) through (d). Nursing majors Non-nursing majors Total Males 97 1017 1114 Females 700 1727 2427 Total 797 2744 3541 1. Find the probability that the student is male or a nursing major P (being male or being nursing major) = 1. Find the probability that the student is female or not a nursing major. P( being female or not a nursing major) = 1. Find the probability that the student is not female or a nursing major P(not being female or being a nursing major) Are the events “being male” and “being a nursing major” mutually exclusive? 1. No, because there are 97 males majoring in nursing 2. No, because one can’t be male and a nursing major at the same time 3. Yes, because one can’t be male and a nursing major at the same time 4. Yes, because there are 97 males majoring in nursing 5. Outside a home, there is a 4-key keypad with the letters a,b,c, and d that can open the garage if the correct 4 letter code is entered. Each key may only be used once, how many possible codes are there? 11 Outside a home, there is an 10-key keypad with letters A, B, C, D, E, F, G and H that can be used to open the garage if the correct ten-letter code is entered. Each key may be used only once. How many codes are possible? The number of possible codes is 10. Outside a home, there is a 4-key keypad with the letters a,b,c, and d that can open the garage if the correct 4 letter code is entered. Each key may only be used once, how many possible codes are there? 12 How many different 10-letter words (real or imaginary) can be formed from the following letters? Z, V, U, G, X, V, H, G, D ten-letter words (real or imaginary) can be formed with the given letters. 12 How many different 10-letter words (real or imaginary) can be formed from the following letters? K, I, B, W, E, Z, I, O, R, Z ten-letter words (real or imaginary) can be formed with the given letters. 12. A horse race has 13 entries and one person owns 2 of those horses. Assuming that there are no ties, what is the probability that those 2 horses finish first and second (regardless of order) 13 A horse race has 13 entries and one person owns 2 of those horses. Assuming that there are no ties, what is the probability that those four horses finish first, second, third, and fourth (regardless of order)? The probability that those two horses finish first, second, third, and fourth is 13 A horse race has 13 entries and one person owns 4 of those horses. Assuming that there are no ties, what is the probability that those four horses finish first, second, third, and fourth (regardless of order)? The probability that those four horses finish first, second, third, and fourth is 13. Determine the required value of the missing probability to make the distribution a discrete probability distribution. 14. 14 Determine the required value of the missing probability to make the distribution a discrete probability distribution. X P(x) 3 0.19 4 ? 5 0.34 6 0.28 P() = (Type an integer or a decimal) 14 Determine the required value of the missing probability to make the distribution a discrete probability distribution. X P(x) 3 0.16 4 ? 5 0.38 6 0.17 P() = (Type an integer or a decimal) 14. A frequency distribution is shown below. Complete a – e. X P(x) 0 0.635 1 0.228 2 0.089 3 0.024 4 0.014 5 0.009 15. Students in a class take a quiz with 8 questions. The number x of questions answered correctly can be approximated by the following probability distribution. Complete a – e. 15 A frequency distribution is shown below. Complete parts (a) through (e). Dogs 0 1 2 3 4 5 Household 1324 436 162 46 27 15 1. Use the frequency distribution to construct a probability distribution. X P(x) 0 1 2 3 4 5 1. Find the mean of the probability distribution µ = (Round to the nearest thousandth as needed.) 1. Find the variance of the probability distribution = (Round to the nearest tenth as needed) 1. Find the standard deviation of the probability distribution • = (Round to the nearest tenth as needed) • e. Interpret the results in the context of the real-life situation. • A. A household on average has 0.5 dog with a standard deviation of 0.9 dog. 1. B. A household on average has 0.5 dog with a standard deviation of 15 dog. 2. C. A household on average has 0.9 dog with a standard deviation of 0.5 dog. 3. D. A household on average has 0.9 dog with a standard deviation of 0.9 dog. 17 Students in a class take a quiz with eight questions. The number x of questions answered correctly can be approximated by the following probability distribution. Complete parts (a) through (e). X 0 1 2 3 4 5 6 7 8 P(x) 0.02 0.02 0.06 0.06 0.14 0.24 0.27 0.12 0.07 (a) Use the probability distribution to find the mean of the probability distribution µ = (b) Use the probability distribution to find the variance of the probability distribution = (c) Use the probability distribution to find the standard deviation of the probability distribution (d) Use the probability distribution to find the expected value of the probability distribution Interpret the results 5. The expected number of questions answered correctly is 5.1 with a standard deviation of 1.8 questions. 6. The expected number of questions answered correctly is 1.8 with a standard deviation of 5.1 questions. 7. The expected number of questions answered correctly is 5.1 with a standard deviation of 0.02 questions. 8. The expected number of questions answered correctly is 3.1 with a standard deviation of 1.8 questions. MATH 221 Homework Week 4

1. 1. The histograms each represents part of a binomial distribution. Each distribution has the same probability of success, p, but different numbers of trials, n. Identify the unusual values of x in each histogram

a. Choose the correct answer below. Use histogram A. X = 0, x = 1, x = 2, x = 3, and x = 4 B. X = 3 and x = 4 C. X = 0 and x = 1 D. There are no unusual values of x in the histogram b. X = 7 A. X = 0, x = 1, x = 2, x = 3, and x = 4 B. X = 0 and x = 1 C. X = 0 and x = 1 D. There are no unusual values of x in the histogram 2 The histograms each represents part of a binomial distribution. Each distribution has the same probability of success, p, but different numbers of trials, n. Identify the unusual values of x in each histogram. (a) N = 4 (b) N = 8

a. Choose the correct answer below. Use histogram (a). A. X = 4 B. X = 0, x =7, and x = 8 C. X = 2 D. There are no unusual values of x in the histogram b. Choose the correct answer below. Use the histogram (b) A. X =0, x =7, and x = 8 B. X = 4 C. X = 4 D. There are no unusual values of x in the histogram 2 The histograms each represents part of a binomial distribution. Each distribution has the same probability of success, p, but different numbers of trials, n. Identify the unusual values of x in each histogram. (a) N = 4 (b) N = 8 a. Choose the correct answer below. Use histogram (a) A. X = 4 B. X = 0, x =7, and x = 8 C. X = 2 D. There are no unusual values of x in the histogram b.Choose the correct answer below. Use the histogram (b) A. X =0, x =7, and x = 8 B. X = 4 C. X = 4 D. There are no unusual values of x in the histogram 2. About 30% of babies born with a certain ailment recover fully. A hospital is caring for 7 babies born with this ailment. The random variable represents the # of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specific the values of n, p , and q, and list the values of random variable x. 3 About 80% of babies born with a certain ailment recover fully. A hospital is caring for five babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. Is the experiment a binomial experiment? Yes No What is a success in this experiment? Baby doesn’t recover Baby recovers This is not a binomial experiment Specify the value of n. Select the correct choice below and fill in any answer boxes in your choice. N = This is not a binomial experiment Specify the value of p. Select the correct choice below and fill in any answer boxes in your choice. P = This is not a binomial experiment Specify the value of q. Select the correct choice below and fill in any answer boxes in your choice. Q = This is not a binomial experiment List the possible values of the random variable x. X = 1, 2, 3,…, 5 X = 0, 1, 2, ….4 X = 0, 1, 2, …5 This is not a binomial experiment 3 About 70% of babies born with a certain ailment recover fully. A hospital is caring for six babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. Is the experiment a binomial experiment? A. No B. Yes What is a success in this experiment? A. Baby recovers B. Baby doesn’t recover C. This is not a binomial experiment Specify the value of n. Select the correct choice below and fill in any answer boxes in your choice. A. N = B. This is not a binomial experiment Specify the value of p. Select the correct choice below and fill in any answer boxes in your choice. p= This is not a binomial experiment Specify the value of q. Select the correct choice below and fill in any answer boxes in your choice. q = This is not a binomial experiment List the possible values of the random variable x. A. X = 0, 1, 2,…,5 B. X = 0, 1, 2,…6 C. X = 1, 2, 3,…6 D. This is not a binomial experiment 3. Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n = 125, p = 0.81 4 Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. N = 129, p = 0.43 The mean, µ is (Round to the nearest tenth as needed.) The variance, is (Round to the nearest tenth as needed.) The standard deviation, is (Round to the nearest tenth as needed.) 4. 56% of men consider themselves professional baseball fans. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Find the probability that the # who consider themselves baseball fans is (a) 8, (b) at least 8, (c) less than 8. 5 Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. N = 121, p = 0.27 The mean, µ is (Round to the nearest tenth as needed.) The variance, is (Round to the nearest tenth as needed.) The standard deviation, is (Round to the nearest tenth as needed.) 5. 45% of households say they would feel secure if they had at least $50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had $50,000 in savings. Find the probability that the # that they say would feel secure is (a) exactly 5, (b) more than 5 or (c) at most 5. 6 48% of men consider themselves professional baseball fans. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Find the probability that the number who consider themselves baseball fans is (a) exactly eight, (b) at least eight, and (c) less than eight. If convenient, use technology to find the probabilities. a. P(8) = (Round to the nearest thousandth as needed) b. P(x≥8) = (Round to the nearest thousandth as needed) c. P(x5) = (Round to three decimal places as needed) c. Find the probability that the number that say they would feel secure is at most five. P(x≤5) = (Round to three decimal places as needed) 7. 24% of college students say they use credit cards. You randomly select 10 students and ask them why they use credit cards because of the rewards program. (a) Exactly 2, (b) more than 2, and (c) between 2 and 5 inclusive. 8 Sixty-five percent of households say they would feel secure if they had $50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had $50,000 in savings. Find the probability that the number that say they would feel secure is (a) exactly five, (b) more than five, and (c) at most five. a. Find the probability that the number that say they would feel secure is exactly five. P(5) = (Round to three decimal places as needed) b. Find the probability that the number sat they would feel secure is more than five. P(x>5) = (Round to three decimal places as needed) c. Find the probability that the number that say they would feel secure is at most five. P(x≤5) = (Round to three decimal places as needed) 8. 34% of women consider themselves of baseball. You randomly select 6 women and ask each if she considers herself a fan of baseball. X p(x) 0 0.083 1 0.255 2 0.329 3 0.226 4 0.087 5 0.018 6 0.002 9 34% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. If convenient, use technology to find the probabilities. a. P(3) = (Round to the nearest thousandth as needed.) b. P(x > 4) = (Round to the nearest thousandth as needed.) c. P(x 4) = (Round to the nearest thousandth as needed.) c. P(x 2) = (Round to the nearest thousandth as needed.) c. P(X 2) = (Round to the nearest thousandth as needed.) c. P(X 635Find the complement of the claim. u 635Find the complement of the claim. u ) = 6. The Gallup Organization contacts 1323 men who are 40-60 years of age and live in the US and asks whether or not they have seen their family doctor.What is the population in the study? Answer:What is the sample in the study? Answer: 7. The ages of 10 brides at their first marriage are given below. 4 32.2 33.6 41.2 43.4 37.1 22.7 29.9 30.6 30.8(a) find the range of the data set. Range = (b) change 43.4 to 58.6 and find the range of the new date set. Range = (c) compare your answer to part (a) with your answer to part (b) 8. The following appear on a physician’s intake form. Identify the level of measurement of the data. (a) Martial Status (b) Pain Level (0-10) (c) Year of Birth (d) Height(a) what is the level of measurement for marital status(b) what is the level of measurement for pain level(c) what is the level of measurement for year of birthWhat is the level of measurement for height 9. To determine her air quality, Miranda divides up her day into 3 parts; morning, afternoon, and evening. She then measures her air quality at 3 randomly selected times during each part of the day. What type of sampling is used? 10. Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The caloric content and the sodium content (in milligrams) for 6 beef hot dogs are shown in the table below. • X= 150 calories • X= 100 calories • X = 120 calories • X = 60 calories

Find the regression equation. = Choose the correct graph below. (a) predict the value of y for x = 150. Answer: (b) predict the value of y for x = 100. Answer: (c) predict the value of y for x = 120. Answer: (d) predict the value of y for x = 60. Answer: 11. A restaurant association says the typical household spends a mean of $4072 per year on food away from home. You are a consumer reporter for a national publication and want to test this claim. You randomly select 12 households and find out how much each spent on food away from home per year. Can you reject the restaurant association’s claim at a = 0.10? Complete parts a through d. • Write the claim mathematically and identify. Choose the correct the answer below. Use technology to find the P-value. P = Decide whether to reject or fail the null hypothesis. Interpret the decision in the context of the original claim. Assume the population is normally distributed. Choose the correct answer below. 12. The table below shows the results of a survey in which 147 families were asked if they own a computer and if they will be taking a summer vacation this year.

(a) find the probability that a randomly selected family is not taking a summer vacation year. Probability = (b) find the probability that a randomly selected family owns a computer Probability = (c) find the probability that a randomly selected family is taking a summer vacation this year and owns a computer Probability = (d) find the probability a randomly selected family is taking a summer vacation this year and owns a computer. Probability = • Are the events of owning a computer and taking a summer vacation this year independent or dependent events? • • 13. Assume the Poisson distribution applies. Use the given mean to find the indicated probability. Find P(5) when ᶙ = 4 P(5) = 14. In a survey of 7000 women, 4431 say they change their nail polish once a week. Construct a 99% confidence interval for the population proportion of women who change their nail polish once a week. A 99% confidence interval for the population proportion is… 15 A random sample of 53 200-meter swims has a mean time of 3.32 minutes and the population standard deviation is 0.06 minutes. Construct a 90% confidence interval for the population mean time. Interpret the results. The 90% confidence interval is Interpret these results. Choose the correct answer: Answer: With 90% confidence, it can be said that the population mean time is between the end points of the given confidence interval. 16. Determine whether the variable is qualitative or quantitative: Weight Quantitative Qualitative 17. 32% of college students say that they use credit cards because of the reward program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the number of college students who say they use credit cards because of the reward program is (a) exactly two, (b), more than two, and (c), between two and five inclusive. (a) P(2) = (b) P(X>2) = (c) P(2

0 notes