# Shape of the distribution of the Sample Mean

CRA CDs, Inc. wants the mean lengths of the "cuts" on a CD to be 135 seconds (2 minutes and 15 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 standard deviation of 8 seconds. Suppose we select a sample of 16 cuts from various CDs sold by CRA CDs, Inc. What can we say about the shape of the distribution of the sample mean? A. 67% of the sample means will be between 127 seconds and 143 seconds. B. 95% of the sample means will be between 127 seconds and 143 seconds. C. 99% of the sample means will be between 127 seconds and 143 seconds. D. 100% of the sample means will be between 127 seconds and 143 seconds. Part c, d, e) Use Excel's NORMDIST function.

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#### Solution Preview

mu = 135, sigma = 8, n = 16

SE = sigma/sqrt n = 8/sqrt 16 = 2

x1 = mu - z * SE = 135 - 2z and x2 = mu + z * SE = ...

#### Solution Summary

The shape of the distribution of the sample mean are determined. A complete, neat and step-by-step solution is provided.