804 CHAPTER 12 Statistics Concept/Writing Exercises 27. Waiting in Line Consider the following illustrations of two bank-customer waiting systems. Old system Bank A Teller 2 Teller 3 Teller 1 Customers Tellers Customers Tellers New system Bank B Teller 2 Teller 3 Teller 1 Enter Here a) How would you expect the mean waiting time in Bank A to compare with the mean waiting time in Bank B? Answers will vary. b) How would you expect the standard deviation of waiting times in Bank A to compare with the standard deviation of waiting times in Bank B? Answers will vary. 28. Can you think of any situations in which a large standard deviation may be desirable? Answers will vary. 29. Can you think of any situations in which a small standard deviation may be desirable? Answers will vary. 30. Without actually doing the calculations, decide which, if either, of the following two sets of data will have the greater standard deviation. Explain why. The first set will have the greater standard deviation because the scores have a greater spread about the mean. 15, 18, 19, 20, 22, 26 21, 22, 22, 23, 23, 24 31. Without actually doing the calculations, decide which, if either, of the following two sets of data will have the greater standard deviation. Explain why. They would be the same, since the spread of data about each mean is the same. 2, 4, 6, 8, 10 102, 104, 106, 108, 110 32. By studying the standard deviation formula, explain why the standard deviation of a set of data will always be greater than or equal to 0. The sum of the values in the − (Data Mean)2 column will always be greater than or equal to 0. 33. Patricia teaches two statistics classes, one in the morning and the other in the evening. On the midterm exam, the morning class had a mean of 75.2 and a standard deviation of 5.7. The evening class had a mean of 75.2 and a standard deviation of 12.5. a) How do the means compare? The mean is the same for both classes. b) If we compare the set of scores from the first class with those in the second class, how will the distributions of the two sets of scores compare? * Challenge Problems/Group Activities 34. Height and Weight Distribution The following chart shown uses the symbol σ to represent the standard deviation. Note that σ2 represents the value that is two standard deviations above the mean; σ −2 represents the value that is two standard deviations below the mean. The unshaded areas, from two standard deviations below the mean to two standard deviations above the mean, are considered the normal range. For example, the average (mean) 8-year-old boy has a height of about 50 inches, but any heights between approximately 45 inches and 55 inches are considered normal for 8-year-old boys. Refer to the chart below to answer the following questions. Inches Pounds Kilogram Centimeters Boys’ physical development, 1–18 years *Supine length to 6 years, standing height from 6 to 18 years Height Weight * 75 65 55 45 35 25 15 180 180 200 160 140 120 100 80 60 40 20 160 140 120 100 60 40 +2V mean mean –2V –2V +2V 85 75 65 55 45 35 25 15 5 Age in years 1 1718 3 5 7 9 111315 80 a) What happens to the standard deviation for weights of boys as the age of boys increases? What is the significance of this fact? The standard deviation increases. There is a greater spread from the mean as they get older. b) Determine the mean weight and normal range for boys at age 13. ≈ Mean: 100 lb; normal range: ≈ 60 to 140 lb c) Determine the mean height and normal range for boys at age 13. Mean: ≈ Mean: 62 in.; normal range: ≈ 53 to 68 in. d) At age 17, what is the mean weight, in pounds, of boys? ≈ 140 lb *See Instructor Answer Appendix
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