Solution Found!
Let X equal the weight (in grams) of a nail of the type
Chapter 5, Problem 5E(choose chapter or problem)
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 \(\bar X\) 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 \(\bar X\).
(b) Let S2 be the sample variance of the nine weights. Find constants a and b so that \(P(a \le S^2 \le b) = 0.90\).
Hint: Because \(8S^2/0.16\) is \(\chi^2(8)\) and \(P(a \le S^2 \le b)\) is equivalent to \(P(8a/0.16 \le 8S^2/0.16 \le 8b/0.16)\), you can find 8a/0.16 and 8b/0.16 in Table IV in Appendix B.
Questions & Answers
QUESTION:
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 \(\bar X\) 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 \(\bar X\).
(b) Let S2 be the sample variance of the nine weights. Find constants a and b so that \(P(a \le S^2 \le b) = 0.90\).
Hint: Because \(8S^2/0.16\) is \(\chi^2(8)\) and \(P(a \le S^2 \le b)\) is equivalent to \(P(8a/0.16 \le 8S^2/0.16 \le 8b/0.16)\), you can find 8a/0.16 and 8b/0.16 in Table IV in Appendix B.
ANSWER:Step 1 of 3
Given:
X represents the weight (in grams) of a nail of the type that is used for making decks.
X follows N(8.78, 0.16).
