## 6.1 The Standard Normal Distribution

A z-score is a standardized value. Its distribution is the standard normal, \(Z \sim N(0, 1)\). 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 \(N(\mu, \sigma)\) then \(z\) tells you how many standard deviations \(x\) is above (greater than) or below (less than) \(\mu\).

## 6.3 Estimating the Binomial with 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 \(\mu\) and the standard deviation \(\sigma\). 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.