# Chapter 5: The Normal Distribution

## Overview

A random variable can be either discrete or continuous. As mentioned in Chapter 4, a discrete random variable can be described by a probability distribution that lists all the possible values of the random variable and their corresponding probabilities. For a continuous random variable, however, we cannot list all the possible values, so a different approach is required to describe the probability distribution. The so-called density curve describes the probability distribution of a continuous random variable**,** and the area under the curve describes probabilities related to continuous random variables. This chapter introduces the normal distribution, one of the most important continuous distributions.

As a result of completing this chapter, you will be able to do the following:

- Describe the properties of a normal density curve.
- Describe the standard normal distribution.
- Use the standard normal table (Table II) in order to:
- Determine the area bounded by some given values under any normal density curve.
- Find values that correspond to given areas under any normal density curve.

- Use a normal probability plot to assess whether a given data set seems to come from a normal population.