ISM_chapter7

# ISM_chapter7 - Chapter 7 Sampling Distributions and the...

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144 Chapter 7: Sampling Distributions and the Central Limit Theorem Instructor’s Solutions Manual 7.9 a. P (| Y μ | .3) = P (–1.2 Z 1.2) = .7698. b. P (| Y μ | .3) = P (–.3 n Z .3 n ) = 1 – 2 P ( Z > .3 n ). For n = 25, 36, 69, and 64, the probabilities are (respectively) .8664, .9284, .9642, and .9836. c. The probabilities increase with n , which is intuitive since the variance of Y decreases with n . d. Yes, these results are consistent since the probability was less than .95 for values of n less than 43. 7.10 a. P (| Y μ | .3) = P (–.15 n Z .15 n ) = 1 – 2 P ( Z > .15 n ). For n = 9, the probability is .3472 (a smaller value). b. For n = 25: P (| Y μ | .3) = 1 – 2 P ( Z > .75) = .5468 For n = 36: P (| Y μ | .3) = 1 – 2 P ( Z > .9) = .6318 For n = 49: P (| Y μ | .3) = 1 – 2 P ( Z > 1.05) = .7062 For n = 64: P (| Y μ | .3) = 1 – 2 P ( Z > 1.2) = .7698 c. The probabilities increase with n .
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ISM_chapter7 - Chapter 7 Sampling Distributions and the...

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