### 6.1 The Standard Normal Distribution

A *z*-score is a standardized value. Its distribution is the standard normal, *Z* ~ *N*(0, 1). The mean of the *z*-scores is zero and the standard deviation is one. If *z* is the *z*-score for a value *x* from the normal distribution *N*(*µ*, *σ*), then *z* tells you how many standard deviations *x* is above—greater than—or below—less than—*µ*.

### 6.2 Using the Normal Distribution

The normal distribution, which is continuous, is the most important of all the probability distributions. Its graph is bell-shaped. This bell-shaped curve is used in almost all disciplines. Since it is a continuous distribution, the total area under the curve is one. The parameters of the normal are the mean *µ* and the standard deviation *σ*. A special normal distribution, called the standard normal distribution, is the distribution of *z*-scores. Its mean is zero, and its standard deviation is one.