The breaking strength of a rivet has a mean value of 10000 p

The breaking strength of a rivet has a mean value of 10,000 psi and a standard deviation of 503 psi.

(a) What is the probability that the sample mean breaking strength for a random sample of 40 rivets is between 9,900 and 10,200? (Round your answer to four decimal places.)


(b) If the sample size had been 15 rather than 40, could the probability requested in part (a) be calculated from the given information? Explain your reasoning.

Yes, the probability in part (a) can still be calculated from the given information.No, n should be greater than 30 in order to apply the Central Limit Theorem.     No, n should be greater than 20 in order to apply the Central Limit Theorem.No, n should be greater than 50 in order to apply the Central Limit Theorem.

You may need to use the appropriate table in the Appendix of Tables to answer this question.

Solution

(a) P(9900 <xbar< 10200)

= P((9900-10000)/(503/sqrt(40)) <(xbar-mean)/(s/vn) <(10200-10000)/(503/sqrt(40)))

=P(-1.26<Z<2.51) = 0.8901 (from standard normal table)

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(b) No, n should be greater than 30 in order to apply the Central Limit Theorem.