ODD ANSWERS A67 19. x = 17Sz ≈ -0.61 21. 0.8997 x = 29Sz ≈ 1.13 x = 8Sz ≈ -1.91 x = 23Sz ≈ 0.26 23. 0.9236 (Tech: 0.9237) 25. 0.0124 27. 0.8944 29. 0.2266 31. 0.2684 (Tech: 0.2685) 33. (a) 0.2061 (Tech: 0.2053) (b) 0.2337 (Tech: 0.2340) (c) 0.3520 (Tech: 0.3526) 35. No unusual events because all of the probabilities are greater than 0.05 37. -0.07 39. 2.455 (Tech: 2.457) 41. 1.04 43. 0.51 45. 119.54 feet 47. 137.80 feet (Tech: 137.81 feet) 49. 136.71 feet (Tech: 136.70 feet) 51. (a) m = 1.5, s ≈ 1.118 (b) Sample Mean 0, 0 0 0, 1 0.5 0, 2 1 0, 3 1.5 1, 0 0.5 1, 1 1 1, 2 1.5 1, 3 2 2, 0 1 2, 1 1.5 2, 2 2 2, 3 2.5 3, 0 1.5 3, 1 2 3, 2 2.5 3, 3 3 (c) mx = 1.5, sx ≈ 0.791 The means are equal, but the standard deviation of the sampling distribution is smaller. 53. mean = 199.6, standard deviation = 44.86 x Mean population density (in people per square mile) μ= 199.6 σ= 44.86 100 140 180 220 260 300 55. (a) 0.1230 (Tech: 0.1223) (b) 0.1675 (Tech: 0.1676) (c) 0.2964 (Tech: 0.2963) The probabilities are smaller. 57. (a) 0.9066 (Tech: 0.9069) (b) 0.0096 (Tech: 0.0097) (c) 0.5521 (Tech: 0.5538) 59. (a) 0.9664 (Tech: 0.9663) (b) 0.9927 (Tech: 0.9926) 61. You cannot use normal distribution because nq 6 5. 63. The probability of getting at least 25 successes; P1x 7 24.52 65. The probability of getting exactly 45 successes; P144.5 6 x 6 45.52 67. The probability of getting less than 60 successes; P1x 6 59.52 69. Can use normal distribution (a) 0.0043 (Tech: 0.0042) x Number of adults μ= 50.4 σ= 3.76 35 40 45 50 55 60 65 x = 40.5 (b) 0.1068 (Tech: 0.1053) x Number of adults μ= 50.4 σ= 3.76 35 40 45 50 55 60 65 x = 49.5 x = 50.5 (c) 0.0036 x Number of adults μ= 50.4 σ= 3.76 35 40 45 50 55 60 65 x = 60.5 Quiz for Chapter 5 (page 290) 1. (a) 0.9535 (b) 0.9871 (c) 0.3616 (d) 0.7703 (Tech: 0.7702) 2. (a) 0.0233 (Tech: 0.0231) (b) 0.9929 (Tech: 0.9928) (c) 0.9198 (Tech: 0.9199) (d) 0.3607 (Tech: 0.3610) 3. 0.0475 (Tech: 0.0478). Yes, the event is unusual because its probability is less than 0.05. 4. 0.2586 (Tech: 0.2611). No, the event is not unusual because its probability is greater than 0.05. 5. 21.19% 6. 503 people (Tech: 505 people) 7. 125 8. 80 9. 0.0049. About 0.5% of samples of 60 people will have a mean IQ score greater than 105. This is a very unusual event. 10. More likely to select one person with an IQ score greater than 105 because the standard error of the mean is less than the standard deviation 11. Can use normal distribution; m = 202.5, s ≈ 6.203 12. (a) 0.3745 (b) 0.8708 (c) 0.0636 No unusual events because all of the probabilities are greater than 0.05 Real Statistics—Real Decisions for Chapter 5 (page 292) 1. (a) 0.4207 (b) 0.9988 2. (a) 0.3264 (Tech: 0.3274) (b) 0.6944 (Tech: 0.6957) (c) randomly selected sample mean 3. Answers will vary.
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