# Central Limit Theorem

If we increase the sample size, n, how does that increased sample size affect our ability to estimate the population mean? How does the population's shape affect the estimate of the mean? Why do so many of life's events share the same characteristics of the Central Limit Theorem?

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#### Solution Preview

(a) When we increase the sample size, n our estimate of the true population mean improves because the standard error of the mean (standard deviation/sqrt n) decreases.

(b) As the sample size increases, the distribution tends to a normal distribution and assumes a bell shape. Now, we are able to make estimates of the mean using the central limit theorem or the empirical rule. This means the shape of the distribution ...

#### Solution Summary

Explains the relationship between population shape and increased sample size on one's ability to estimate population mean. Relates question to Central Limit Theorem.