Central Limit Theorem

By way of a quick review of the previous section, the law of large numbers tells us that as our sample gets larger, the closer our sample mean matches up with the population average. While this tells us what we should expect the value of the sample mean to be, it does not tell us anything at all about the distribution. For that, we need the central limit theorem. The central limit theorem (CLT) states that if we have a large enough sample size, the distribution of the sample mean is approximately normal, with a mean of the population mean and a standard deviation of the population standard deviation divided by the square root of n. This is important because not only do we know the typical value that our population mean can take, but we know the shape and variance of the distribution as well.

Normal Distribution and the CLT

In Chapter 8, Foundational Probability Concepts and Their Applications, we looked at a type of continuous distribution known as normal...