7.13: Solutions
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1.
- U(24, 26), 25, 0.5774
- N(25, 0.0577)
- 0.0416
3. 0.0003
5. 25.07
7.
- N(2,500, 5.7735)
- 0
9. 2,507.40
13. N(10,108))
15. 0.7799
17. 1.69
19. 0.0072
21. 391.54
23. 405.51
25. Mean = 25, standard deviation = 2/7
26. Mean = 48, standard deviation = 5/6
27. Mean = 90, standard deviation = 3/4
28. Mean = 120, standard deviation = 0.38
29. Mean = 17, standard deviation = 0.17
30. Expected value = 17, standard deviation = 0.05
31. Expected value = 38, standard deviation = 0.43
32. Expected value = 14, standard deviation = 0.65
33. 0.23
34. 0.060
35. 1/5
36. 0.063
37. 1/3
38. 0.056
39. 1/10
40. 0.042
41. 0.999
42. 0.901
43. 0.301
44. 0.832
45. 0.483
46. 0.500
47. 0.502
48. 0.519
49.
- Χ = amount of change students carry
- Χ ~ E(0.88, 0.88)
- X–𝑋– = average amount of change carried by a sample of 25 students.
- X–𝑋– ~ N(0.88, 0.176)
- 0.0819
- 0.1882
- The distributions are different. Part a is exponential and part b is normal.
51.
- length of time for an individual to complete IRS form 1040, in hours.
- mean length of time for a sample of 36 taxpayers to complete IRS form 1040, in hours.
- N(10.53, 13)(10.53, 13)
- Yes. I would be surprised, because the probability is almost 0.
- No. I would not be totally surprised because the probability is 0.2312
53.
- the length of a song, in minutes, in the collection
- U(2, 3.5)
- the average length, in minutes, of the songs from a sample of five albums from the collection
- N(2.75, 0.066)
- 2.74 minutes
- 0.03 minutes
55.
- True. The mean of a sampling distribution of the means is approximately the mean of the data distribution.
- True. According to the Central Limit Theorem, the larger the sample, the closer the sampling distribution of the means becomes normal.
- The standard deviation of the sampling distribution of the means will decrease making it approximately the same as the standard deviation of X as the sample size increases.
57.
- X = the yearly income of someone in a third world country
- the average salary from samples of 1,000 residents of a third world country
- X–𝑋– ∼ N(2000, 80001000√)(2000, 80001000)
- Very wide differences in data values can have averages smaller than standard deviations.
- The distribution of the sample mean will have higher probabilities closer to the population mean.
P(2000 < X–𝑋– < 2100) = 0.1537
P(2100 < X–𝑋– < 2200) = 0.1317
59.
b
60. 64
61.
- Yes
- Yes
- Yes
- 0.6
62. 400
63. 2.5
64. 25
65. 0.0087
66. 0.0064, 0.0064
67.
- It has no effect.
- It is divided by 2–√2.
- It is divided by 2.
68.
69.
70. 0.955
71. 0.927
72. 0.648
73. 0.101
74. 0.273