Chapter 5: The Normal Distribution


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.

Learning Objectives

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.


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