Suppose that a random sample of size 64 is to be selected from a population with

Question

Suppose that a random sample of size 64 is to be selected from a population with mean 40 and standard deviation 5. (a) What are the mean and standard deviation of the x sampling distribution? =40 CF = 10.625 (b) What is the approximate probability that x will be within 0.3 of the population mean ? (Round your answer to four decimal places.) p = 0.3688 c) What is the approximate probability that x will differ from by more than 0 87(Round your answer to four decimal places. p = 0.8997 You may need to use the appropriate table in Appendix A to answer this question.

Explanation / Answer

c) P(X bar will differ from mean by more than 0.8) = 1 - P(X bar will be within 0.8 of the mean)

                                               = 1 - P(-0.8/0.625 < Z < 0.8/0.625)

                                               = 1 - P(-1.28 < Z < 1.28)

                                               = 1 - (P(Z < 1.28) - P(Z < -1.28))

                                               = 1 - (0.8997 - 0.1003)

                                               = 0.2006 (ans)

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