The breaking strength of a rivet has a mean value of 10,000 psi and a standard d

Question

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? (Give answer accurate to 3 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, according to the Rule of Thumb n should be greater than 30 in order to apply the C.L. T. No, according to the Rule of Thumb n should be greater than 25 in order to apply the C.L.T. No, according to the Law of Large Numbers n should be greater than 30 in order to apply the C.L.T You may need to use the appropriate table in the Appendix of Tables to answer this question

Explanation / Answer

Solution:- mean = 10000 , sd = 503

a) n = 40 Z = (X - mu)/(sd/sqrt(n))

P(9900 < X < 10200) = P((9900 - 10000)/(503/sqrt(40) < Z < (10200 - 10000)/(503/sqrt(40) )

= P(-1.2574 < Z < 2.5147)

=  0.890

b) option B. No, n should be greater than 30 in order to apply the C. L. T.

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