A64 ODD ANSWERS 5. Answers will vary. Similarities: The two curves will have the same line of symmetry. Differences: The curve with the larger standard deviation will be more spread out than the curve with the smaller standard deviation. 7. m = 0, s = 1 9. “The” standard normal distribution is used to describe one specific normal distribution 1m = 0, s = 12. “A” normal distribution is used to describe a normal distribution with any mean and standard deviation. 11. No, the graph is skewed left. 13. No, the graph is symmetric but it is not bell shaped. 15. Yes, the graph fulfills the properties of the normal distribution. m ≈ 11.5, s ≈ 1.5 17. 0.7257 19. 0.0228 21. 0.4878 23. 0.6293 25. 0.0470 27. 0.7422 29. 0.6387 31. 0.4979 33. 0.8788 35. 0.2006 (Tech: 0.2005) 37. (a) Distance (in miles) 5 4 3 2 1 6 32,353 37,046 41,739 46,432 27,660 Life Spans of Tires Frequency It is reasonable to assume that the life spans are normally distributed because the histogram is symmetric and bell-shaped. (b) 37,234.7; 6259.2 (c) The sample mean of 37,234.7 hours is less than the claimed mean, 40,000 on average; the tires in the sample lasted for a shorter time. The sample standard deviation of 6259.2 is greater than the claimed standard deviation, so the tires in the sample had a greater variation in life span than the manufacturer’s claim. 39. (a) x = 98Sz ≈ -0.125 x = 65Sz ≈ -2.188 x = 106Sz ≈ 0.375 x = 124Sz ≈ 1.50 (b) x = 65 is unusual because the corresponding z-score 1-2.1882 lies more than 2 standard deviations away from the mean. 41. 0.2660 43. 0.9832 45. 0.6826 (Tech: 0.6827) 47. 0.7019 49. 0.0148 51. 0.3133 53. 0.9250 (Tech: 0.9249) 55. 0.0098 (Tech: 0.0099) 57. 36 48 60 72 84 The normal distribution curve is centered at its mean (60) and has 2 points of inflection (48 and 72) representing m { s. 59. (1) The area under the curve is 1b - a2a 1 b - ab = b - a b - a = 1. (Because a 6 b, you do not have to worry about division by 0.) (2) All of the values of the probability density function are positive because 1 b - a is positive when a 6 b. Section 5.2 (page 249) 1. 0.4207 3. 0.3446 5. 0.1787 (Tech: 0.1788) 7. (a) 0.0183 (b) 0.5103 (Tech: 0.5119) (c) 0.0228 The events a and c are both unusual because the probability is less than 0.05. 9. (a) 0.1515 (b) 0.6536 (Tech: 0.6528) (c) 0.0918 None of the events are unusual because none of the probabilities are less than 0.05. 11. (a) 0.0062 (b) 0.7492 (Tech: 0.7499) (c) 0.0004 13. 0.3288 (Tech: 0.3276) 15. 0.0324 (Tech: 0.0325) 17. (a) 86.86% (Tech: 86.96%) (b) 464 scores (Tech: 465 scores) 19. (a) 98.93% (b) 75.75% (Tech: 75.76%) (c) 6 mothers 21. Out of control, because there is a point more than three standard deviations beyond the mean 23. Out of control, because there are nine consecutive points below the mean, and two out of three consecutive points lie more than two standard deviations from the mean Section 5.3 (page 257) 1. -0.81 3. 0.45 5. -1.645 7. 1.04 9. -0.44 11. 1.96 13. -0.67 15. 1.34 17. -0.38 19. 1.99 21. -1.645, 1.645 23. -1.18 25. -0.35 27. -2.00 29. 1.28 31. (a) 247.8 pounds (b) 158.1 pounds (c) 133.42 pounds 33. (a) 133.94 seconds (b) 156.74 seconds (Tech: 156.60) (c) 210.04 seconds 35. (a) 664.5 (b) 432.5 and 567.5 37. (a) 5.67 million cells per microliter (b) Red blood cell counts less than 4.74 million or greater than 6.06 million 39. 32.61 ounces 41. 7.93 ounces Section 5.4 (page 269) 1. 150, 3.571 3. 790, 3.036 5. False. As the size of a sample increases, the mean of the distribution of sample means does not change. 7. False. A sampling distribution is normal when either n Ú 30 or the population is normal. 9. (c), because mx = 16.5, sx = 1.19, and the graph approximates a normal curve.
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