Question

The population mean and standard deviation are given below. Find the indicated probability and determine whether a sample mean in the given range below would be considered unusual. If​ convenient, use technology to find the probability.

For a sample of n= 3131​,find the probability of a sample mean being less than 12,751or greater than 12,754 when μ=12,751and σ=1.9

For the given​ sample, the probability of a sample mean being less than 12,751 or greater than 12,754 is ________. (Round to four decimal places as​ needed.)

Would the given sample mean be considered​ unusual?

A.The sample mean would be considered unusual because there is a probability greater than 0.05 of the sample mean being within this range.

B.The sample mean would not be considered unusual because there is a probability greater than 0.05 of the sample mean being within this range.

C.The sample mean would be considered unusual because there is a probability less than 0.05 of the sample mean being within this range.

D.The sample mean would not be considered unusual because there is a probability less than 0.05 of the sample mean being within this range.

Answer 1

Refer Standard normal table/Z-table to find the probability or use excel formula "=NORM.S.DIST(0, TRUE)" & "=NORM.S.DIST(8.79, TRUE)" to find the probability.

For the given​ sample, the probability of a sample mean being less than 12,751 or greater than 12,754 is .

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The sample mean would not be considered unusual because there is a probability greater than 0.05 of the sample mean being within this range.