12. FILE Scrapper Elevator Company has 20 sales representatives who sell its product throughout the United States and Canada. The number of units sold last month by each representative is listed below. Assume these sales figures to be the population values. 2 3 2 3 3 4 2 4 3 2 2 7 3 4 5 3 3 3 3 5 a. Draw a graph showing the population distribution. b. Compute the mean of the population. c. Select five random samples of five each. Compute the mean of each sample. Use the methods described in this chapter. Using a random number table (Appendix B.4) or statistical software, select the items to be included in the sample. d. Compare the mean of the sampling distribution of the sample mean to the population mean. Would you expect the two values to be about the same? e. Draw a histogram of the sample means. Why are the two distributions different? requency

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The manager of Hudson Auto Repair would like to get a better picture of the distribution of costs for new parts used in the engine tune-up jobs done in the garage. A sample of 50 customer invoices for tune-ups has been taken and the costs of parts, rounded to the nearest dollar, are listed below. 91 78 93 57 75 52 99 80 73 62 71 69 72 89 66 75 79 75 72 76 104 74 62 68 97 105 77 65 80 109 85 97 88 68 83 68 71 69 67 74 62 82 98 101 79 105 79 69 62 73 Develop a frequency distribution for these cost data. Use your own judgment to determine the number of classes and class width that provide a distribution that will be meaningful and helpful to the manager. a. Develop a stem-and-leaf display showing both the rank order and shape of the data set. (3) b. Develop a stretched stem-and-leaf display using two stems for each leading digit(s). (2) c. Which display is better at revealing the natural grouping and variation in the data? (1)

You decide that you want to make sure your estimate from part a is correct. You go out and gather 10 simple random samples of 25 people in your school and calculate the proportion of students within each sample whose Amazon packages arrive within two business days of ordering.  The proportion of customers that receive their packages within two days of ordering are given below.  0.70, 0.75, 0.6, 0.95, 0.90, 0.73, 0.87, 0.86, 0.92, 0.97 Explain why all of the sample proportions are not the same.