Central Limit Theorem

[mattc]

Please help with the following question. Thanks a bunch!

Explain what the Central Limit Theorem implies in your own words. Why is it important?

[omega]

The Central Limit Theorem implies that if you take a lot of samples from a certain probability distribution, the distribution of the mean will be approximately normal, even if the original distribution was not normal. And the standard deviation of the mean distribution is s/sqrt(n).

When testing a hypothesis or calculating a confidence interval, we use the mean of a certain number of samples, and assume that the mean follows a normal distribution. The Central Limit Theorem tells us that this assumption is approximately correct for large samples, and tells us the standard deviation to use.