# Z Score

Assume that men's weights are normally distributed with a mean of 172 lbs. and a standard deviation of 29 lbs.

I understand that if one man is selected the probability his weight is less than 182 lbs is .6331

However I don't understand if 25 men are randomly selected what is the probability that they have a mean weight less than 182 lbs.

I know the answer is .9573 but I do not understand how to get it.

Please explain.

© BrainMass Inc. brainmass.com October 9, 2019, 10:10 pm ad1c9bdddfhttps://brainmass.com/statistics/central-limit-theorem/central-limit-theorem-understanding-score-210482

#### Solution Preview

To find the answer, we're going to use z-scores again. Here, instead of having a raw score that we're comparing to a population mean, we have a sample mean (182) for a sample of 25 men that we're comparing to a ...

#### Solution Summary

The expert understands the z score using the Central Limit Theorem.

$2.19