Chapter 07 - Continuous Probability Distributions

Continuous Probability Distributions

7. The actual shape of a normal distribution depends on its mean and standard deviation. Thus, there is a normal distribution, and an accompanying normal curve, for a mean of 7 and a standard deviation of 2. There is another normal curve for a mean of $25,000 and a standard deviation of $1,742, and so on. (LO7-2)

8. It is bell shaped and symmetrical about its mean. It is asymptotic. There is a family of normal curves. The mean, median, and the mode are equal. (LO7-2)

9. a. 490 and 510, b. 480 and 520, c. 470 and 530, (LO7-3)

10. a. about 68 percentb. about 95 percentc. over 99 percent (LO7-3)

11. ZRob = -2 Z Rachel = 1.875Adjusting for their industries, Rob is well below average and Rachel well above. (LO7-3)

12.

The first is slightly less expensive than average and the second is slightly more. (LO7-3)

13. a. 1.25 b. 0.3944, c. 0.3085,

14. a. z = 0.84b. 0.2995c. 0.1894 (LO7-3)

15. a. 0.3413, b. 0.1587, c. 0.3336 (LO7-3)

16. a. About 0.4332 from Appendix B.3, where z = 1.50b. About 0.1915, where z = – 0.50c. About 0.3085, found by 0.5000 – 0.1915 (LO7-3)

17. a. 0.8276,b. 0.1056,c. 0.2029, (LO7-3)

18. a. 0.4017c. 0.2022 (LO7-3)

19. a. 0.4129.

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Chapter 07 - Continuous Probability Distributions

b. 0.2794.c. 0.8190. (LO7-3)

20 a 0.2620.b. 0.8849,c. 0.0139 (LO7-3)

21. a. 0.0764, b. 0.9236, c. 0.0.362. (LO7-3)

22. a. 0.1335,b. 0.1965, c. 0.4575, (LO7-3)

23. X = 56.60, (LO7-3)

24. (LO7-3)

25. 1630, found by 2100 1.88(250) (LO7-3)

26. 1884, found by 1500 + 1.28(300) (LO7-3)

27. a. 215, found by 195 + 2.33(8.5)b. 270, found by 290 – 2.33(8.5) (LO7-3)

28. 34,314; found by 26,889 + 1.65(4500) (LO7-3)

29. 41.7%, found by .12 + 1.65(.18) (LO7-3)

30. 10,289; found by 12,200 – 2.33(820) (LO7-3)

45. a. – 0.4 for net sales, b. Net sales are 0.4 standard deviations below the mean. Employees is 2.92 standard

deviations above the mean.c. 65.54% of the aluminum fabricators have greater net sales compared with Clarion,

(LO7-3)

46. a.

b. 0.7745, c. 0.0495,d. 35.3, (LO7-3)

47. a. 0.5000,b. 0.2514, c. 0.6374, d. 0.3450, (LO7-3)

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Chapter 07 - Continuous Probability Distributions

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Chapter 07 - Continuous Probability Distributions

48. a. 0.4082, b. 0.0918, c. 0.0905, d. 0.6280, e. 5.25, (LO7-3)

49. a. 0.3015, b. 0.2579, c. 0.0011, d. 1818, (LO7-3)

50. a. 0.3446, b. 0.6006, c. 0.1039, d. 44,200, (LO7-3)

51. a. 0.9082, b. 0.7823, c. Prob(Z > x) = 0.01 implies Prob (0 < Z < x) = 0.49 and x = 2.33

Women: 34 + 2.33(4.5) = 44.485Men: 29 + 2.33(5.1) = 40.883 (LO7-3)

52. a. 0.1314 or 13.14%,b. 0.1189 or 11.89%, c. 0.0136 or 1.36%, (LO7-3)

53. About 4099 units found by solving for X. 1.65 = (X – 4000)/60 (LO7-3) 54. a. 0.0047,

b. 0.1241, c. 0.8413,

d. No, because (LO7-3)

55. a. 15.39%,b. 17.31%, c. Yes, but it is rather remote. Reasoning: On 99.73% of the days, returns are between

3.55 and 17.05, found by 10.3 3(2.25). Thus, the chance of less than 3.55 returns is rather remote. (LO7-3)

61. a. =36.75b. =28.5c. 0.5596 (LO7-3)

62. a. 0.0091, b. 0.0062, c. 0.9847,

63. a. 21.19 percent

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Chapter 07 - Continuous Probability Distributions

b. Increase the mean. z = (9.00 – 9.25)/0.25 = –1.00; probability is 0.5000 – 0.3413 = 0.1587 Reduce the standard deviation. z = (9.00 – 9.20)/0.15 = 1.33; the probability = 0.500 – 0.4082 = 0.0918Reducing the standard deviation is better because a smaller percent of the hams will be below the limit. (LO7-3)

64. 0.5000 – 0.3333 = 0.1667 so z = 0.43 =9.07

0.5000 – 0.2000 = 0.3000, so z = 0.84 =6.07

There is about a 50 percent difference between the two standard deviations. The distribution is not normal. (LO7-3)

65. a. 0.0548b. 55,350c. 0.0808 (LO7-3)

66. a. It is over $45 about 22 days, found by 240(0.0918).b. 14.92 percent of the days.c. $44.34, (LO7-3)

67. =29,126 and =462,718 (LO7-3)

68. 32.56 (LO7-3)

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