A54 ODD ANSWERS 55. (a) P ≈ -2.61 The data are skewed left. (b) P ≈ 4.12 The data are skewed right. (c) P = 0 The data are symmetric. (d) P = 1 The data are skewed right. (e) P = -3 The data are skewed left. Section 2.4 Activity (page 100) 1. When a point with a value of 15 is added, the mean remains constant or changes very little, and the standard deviation decreases. When a point with a value of 20 is added, the mean is raised and the standard deviation increases. 2. To get the largest standard deviation, plot four of the points at 30 and four of the points at 40. To get the smallest standard deviation, plot all of the points at the same number. That way, each x - x is 0, so the standard deviation will be 0. Section 2.5 (page 109) 1. The talk is longer in length than 75% of the lectures in the series. 3. The student’s grade on the Fundamentals of Engineering exam was below the average. 5. The interquartile range of a data set can be used to identify outliers because data entries that are greater than Q3 + 1.51IQR2 or less than Q1 - 1.51IQR2 are considered outliers. 7. True 9. False. An outlier is any number above Q3 + 1.51IQR2 or below Q1 - 1.51IQR2. 11. (a) Q1 = 57, Q2 = 60, Q3 = 63 (b) IQR = 6 (c) 80 13. Min = 0, Q1 = 2, Q2 = 5, Q3 = 8, Max = 10 15. (a) Min = 24, Q1 = 28, Q2 = 35, Q3 = 41, Max = 60 (b) 20 2428 35 41 60 25 30 35 40 45 50 55 60 17. (a) Min = 1, Q1 = 4.5, Q2 = 6, Q3 = 7.5, Max = 9 (b) 0123456789 4.5 1 6 7.5 9 19. None. The data are not skewed or symmetric. 21. Skewed left. Most of the data lie to the right on the box plot. 23. 1 2 3 6.5 8 Number of hours 2 4 6 8 1 3 5 7 Studying 25. Distance (in miles) 1 3 7 12 45 Commuting Distances 0 5 1015202530354045 27. (a) 6.5 hours (b) about 50% (c) about 25% 29. About 158; About 65% of quantitative reasoning scores on the Graduate Record Examination are less than 158. 31. About 7th percentile; About 7% of quantitative reasoning scores on the Graduate Record Examination are less than 140. 33. 10th percentile 35. 57, 57, 61, 61, 65, 66 37. 10 4 8 1216202428 20 30 40 50 60 70 80 90 100 Percentile Time (in minutes) Depatment of Motor Vehicles Wait Times 39. About 85th percentile 41. ASz = -1.43 BSz = 0 CSz = 2.14 A z-score of 2.14 would be unusual. 43. Not unusual; The z-score is 0.91, so the age of 31 is about 0.91 standard deviation above the mean. 45. Not unusual; The z-score is -0.26, so the age of 27 is about 0.26 standard deviation below the mean. 47. Unusual; The z-score is -2.32, so the age of 20 is about 2.38 standard deviations below the mean. 49. (a) For 34,000, z ≈ -0.44; For 37,000, z ≈ 0.89; For 30,000, z ≈ -2.22 The tire with a life span of 30,000 miles has an unusually short life span. (b) For 30,500, about 2.5th percentile; For 37,250, about 84th percentile; For 35,000, about 50th percentile 51. Gary Oldman: z ≈ 1.75; Sam Rockwell: z ≈ -0.09; The age of Gary Oldman was between 1 and 2 standard deviations above the mean age of Best Actor winners, and the age of Sam Rockwell was less than 1 standard deviation below the mean age of Best Supporting Actor winners. Neither actor’s age is unusual.
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