# Sampling distribution of a sample mean

CRA CDs Inc. wants the mean lengths of the "cuts" on a CD to be 145 seconds (2 minutes and 25 seconds). This will allow the disk jockeys to have plenty of time for commercials within each 10-minute segment. Assume the distribution of the length of the cuts follows the normal distribution with a population standard deviation of 10 seconds. Suppose we select a sample of 24 cuts from various CDs sold by CRA CDs Inc.

(b) What is the standard error of the mean? (Round your answer to 2 decimal places.)

(c) What percent of the sample means will be greater than 150 seconds? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

(e) What percent of the sample means will be greater than 138 but less than 150 seconds? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

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#### Solution Summary

A calculation of probability based on sampling distribution of sample proportion is given in the answers, which are in an attached Word file.