Let X equal the weight (in grams) of a nail of the type that is used for making decks

Chapter 5, Problem 5.5-5

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Let X equal the weight (in grams) of a nail of the type that is used for making decks. Assume that the distribution of X is N(8.78, 0.16). Let X be the mean of a random sample of the weights of n = 9 nails.(a) Sketch, on the same set of axes, the graphs of the pdfs of X and of X. (b) Let S2 be the sample variance of the nine weights. Find constants a and b so that P(a S2 b) = 0.90. Hint: Because 8S2/0.16 is 2(8) and P(a S2 b) is equivalent to P(8a/0.16 8S2/0.16 8b/0.16), you can find 8a/0.16 and 8b/0.16 in Table IV in Appendix B.