# Probability distribution of a sample mean

A wholesaler assures retailer replacement times for TVs normally dist. with mean of 8.2 and s.d. of 1.1. The retailer finds that a random sample of 20 sets from the wholesaler have mean replacement time of 7.6 years. Find P of getting a sample of 20 TVs with a mean replacement time of 7.6 years or less.

Is wholesaler trustworthy?

https://brainmass.com/statistics/central-limit-theorem/probability-distribution-sample-mean-26782

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

Please see the attached Word document for calculations and explanation of this exercise.

Solution:

First, organize the information given in the problem.

The question is: Find

We know the mean and standard deviation of from the Central Limit Theorem, so we can solve this just like any other Normal distribution problem. We subtract the mean and divide by the standard deviation of to find a Z-score.

Is wholesaler trustworthy?

The wholesaler is probably not trustworthy. If he is, we have just seen an event with probability of 0.0073. We must either believe we have seen an event that would happen by chance only about 7 times in 1000 or we must conclude that the wholesaler is not trustworthy ( is likely to be less than 8.2).

Â© BrainMass Inc. brainmass.com September 26, 2022, 5:38 pm ad1c9bdddf>https://brainmass.com/statistics/central-limit-theorem/probability-distribution-sample-mean-26782