# Chapter 4 The distribution of the sample mean

Given a sample of data, it can be very useful to ascertain what the associated ** distribution of the sample mean** would be. Once we know what this distribution is, it makes it much easier to draw conclusions, or make inferences, about the population mean based on our sample.

In this chapter, we discuss how to ascertain the distribution of the sample mean. We will rely on the Central Limit Theorem, and consider the following three scenarios:

- It is known that the underlying population distribution is normal
- The underlying population distribution is not known, and the sample size is 30 or more
- The underlying population distribution is not known, and the sample size is less than 30