2-2 Standard Normal Calculations

Def. The standard normal distribution is a normal distribution with
= 0 and = 1.

A random variable with a standard normal distribution is called a standard normal random variable and is denoted by Z. The sample Z – score for a measurement is

The population Z – score for a measurement is.

The value Z describes the number of standard deviations between x and .

The probability distribution for a normal random variable is

For the distribution of Z, the normal density formula is

Def. A normal probability plot for a data set is a scatterplot with the ranked data values on one axis and their corresponding expected Z-scores on the other axis.

Basic Properties of the Standard Normal Curve

1. The total area under the standard curve is equal to one (1).

2. The standard normal curve extends infinitely in both directions with the horizontal axis as an asymptote.

3. There exists symmetry about .

4. Most (99+%) of the area lies between –3 and 3.