# Probability regarding a sample mean (central limit theorem)

Question: Men have hips normally dist. with a mean of 14.4 in. & s.d. of 1.0. Assume 2 male riders randomly selected. Find the probability that their mean hip width is greater than 15.5 in. Please show steps to arrive at the solution

Also: Is the design appropriate assuming that the 2 men have a mean breadth of 16.75 inches?

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

This solution finds the probability of an event related to a sample mean by applying the central limit theorem. Please see the attached Word document for solution details.

Solution:

If a sample of n observations is taken from a normal distribution and you want to make inferences about , the mean of those n observations, use this distribution:

.

First list what is given in the problems

The question is: Find .

IS the design appropriate assuming 2 men have a mean breadth of 16.75 inches?

I'm not sure about this, since some of the details of the problem may have been omitted but I'm assuming you want to find .

If the mean of the 2 men have a breadth of 16.75 inches, the sample is very unlikely to have come from a population with . We have either seen a very rare event or the true population mean is greater than 14.4.

Â© BrainMass Inc. brainmass.com September 26, 2022, 6:23 pm ad1c9bdddf>https://brainmass.com/statistics/central-limit-theorem/probability-regarding-sample-mean-central-limit-theorem-26787