780 APPENDIX D graph is misleading in the sense that it creates the false impression that actual enrollments are far below the goal, which is not the case. Fox News apologized for their graph and provided a corrected graph. 6. Two wins is not significantly high because P12 or more wins2 = 0.380, which is not low (0.05 or less). The probability of making a profit with two or more wins is 0.380, which is not very likely. Things aren’t looking too good for this gambler. 7. a. 0.254 b. 0.255 (Table: 0.256) c. m = 5.6 adults, s = 1.3 adults d. Yes. Using the range rule of thumb, 1 is less than m - 2s = 3.0; using probabilities, the probability of 1 or fewer is 0.00129 (Table: 0.001), which is low, such as less than 0.05. 8. Not a probability distribution because the responses are not values of a numerical random variable. Chapter 6 Answers Section 6-1 1. The word “normal” has a special meaning in statistics. It refers to a specific bell-shaped distribution that can be described by Formula 6-1. The lottery digits do not have a normal distribution. 3. The mean is m = 0 and the standard deviation is s = 1. 5. 0.4 7. 0.2 9. 0.6700 11. 0.6993 (Table: 0.6992) 13. 1.23 15. -1.45 17. 0.0228 19. 0.9082 21. 0.1587 23. 0.9599 25. 0.0441 (Table: 0.0440) 27. 0.1021 29. 0.8789 (Table: 0.8788) 31. 0.9770 (Table: 0.9771) 33. 0.9999 (Table: 0.9999 or 0.9998) 35. 0.9999 (Table: 0.9998) 37. 2.33 39. -2.33, 2.33 41. 0.67 43. 2.05 45. 68.27% (Table: 68.26%) 47. 99.73% (Table: 99.74%) 49. a. 2.28% b. 2.28% c. 95.45% (Table: 95.44%) Section 6-2 1. a. m = 0; s = 1 b. The z scores are numbers without units of measurement. 3. No. A standard normal distribution has a mean of 0 and a standard deviation of 1, but the distribution described in the preceding exercise has a mean different from 0 and a standard deviation different from 1. The distribution is a normal distribution, but not a standard normal distribution. 5. 0.8849 7. 0.9053 9. 136 11. 69 13. 0.1978 (Table: 0.1977) 15. 0.3156 17. 0.5252 19. 0.4504 (Table: 0.4489) 21. 84.1 beats per minute 23. 43.3 beats per minute and 95.9 beats per minute. No, 90 beats per minute is not significantly high. 25. a. 72.11% (Table: 72.23%). Yes, about 28% of women are not qualified because of their heights. b. 58.2 in. to 69.2 in. 27. a. 0.92% (Table: 0.90%). Because so few men can meet the height requirement, it is likely that most Mickey Mouse characters are women. b. 64.0 in. to 68.6 in. 29. 539.9 mm and 600.1 mm 31. 16.4 in. 10. Yes. If using the range rule of thumb, significantly high numbers of sleepwalkers are greater than or equal to m + 2s = 1.5 + 211.02 = 3.5 sleepwalkers, and 4 sleepwalkers is greater than or equal to 3.5 sleepwalkers. If using probabilities, the probability of 4 or more sleepwalkers is 0.029, which is small (less than 0.05). Chapter 5: Review Exercises 1. 0.0563 2. 0.349 3. m = 0.4 workers and s = 0.6 workers. 4. No, 0 is not significantly low. If using the range rule of thumb with m = 0.4 workers and s = 0.6 workers, values are significantly low if they are less than or equal to m - 2s = -0.8, but 0 is not less than or equal to -0.8. If using probabilities, the probability of 0 workers testing positive is 0.651, which is not low (less than or equal to 0.05). 5. Yes, 4 is significantly high. If using the range rule of thumb with m = 0.4 workers and s = 0.6 workers, values are significantly high if they are greater than or equal to m + 2 s = 1.6, and 4 is greater than or equal to 1.6. If using probabilities, the probability of 4 or more workers testing positive is 0.000533, which is low (less than or equal to 0.05). 6. No. The responses are not numerical as required. 7. No, because ΣP1x2 = 0.9686, but the sum should be 1. (There is a little leeway allowed for rounding errors, but the sum of 0.9686 is too far from 1.) 8. Yes, probability distribution with m = 4.6 people, s = 1.0 people. (The sum of the probabilities is 0.999, but that is due to rounding errors.) 9. a. 236.0 checks b. m = 236.0 checks and s = 12.8 checks c. 210.4 checks (or 210.3 checks if using the unrounded s) d. Yes, because 0 is less than or equal to 210.4 checks (or 210.3 checks). 10. a. 7>365 or 0.0192 b. 0.981 c. 0.000182 d. No, because the event is so rare. (But it is possible that more than one death occurs in a car crash or some other such event, so it might be wise to consider a contingency plan.) Chapter 5: Cumulative Review Exercises 1. a. 9.6 moons b. 5.0 moons c. 0 moons d. 28.0 moons e. 11.0 moons f. 120.3 moons2 g. -12.4 moons, 31.6 moons h. No, because none of the planets have a number of moons less than or equal to -12.4 moons (which is impossible, anyway) and none of the planets have a number of moons equal to or greater than 31.6 moons. i. Ratio j. Discrete 2. a. 1>10,000 or 0.0001 b. 0.0365 c. 0.964 d. -75. 3. a. 0.270 b. 0.373 c. 0.0726 d. 0.691 e. 0.627 4. a. 663 b. 557 c. 24.4% d. Statistic 5. No vertical scale is shown, but a comparison of the numbers shows that 7,066,000 is roughly 1.2 times the number 6,000,000; however, the graph makes it appear that the goal of 7,066,000 people is roughly 3 times the number of people enrolled. The
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