# Central Limit Theorem and Population Shape

1. State the main points of the Central Limit Theorem for a mean.

2. Why is population shape of concern when estimating a mean? What does sample size have to do with all?

© BrainMass Inc. brainmass.com June 3, 2020, 5:26 am ad1c9bdddfhttps://brainmass.com/statistics/central-limit-theorem/central-limit-theorem-population-shape-297562

#### Solution Preview

Central Limit Theorem

The central limit theorem states that as the sample size (or number of observations in each sample) increases to large enough, the sampling distribution of the mean can be approximated by the normal distribution. This is true regardless of the shape of the distribution of the individual values in the population.

Some important points regarding the central limit theorem are listed below:

(1) For most population distributions, regardless of shape, the ...

#### Solution Summary

This solution states the main points of the central limit theorem and why the population shape can be of concern.