The Normal Distribution

Probability Distribution for a Normal Random Variable x

where

Mean of the normal random variable x

Standard deviation

3.1416...

2.71828...

Definition 5.1

The standard normal distribution is a normal distribution with and . A random variable with a standard normal distribution, denoted by the symbol z, is called a standard normal random variable.

Normal distributions as probability distributions

In the language of random variables, if x has the

N(, ) distribution, then the standardized variable

is a standard normal random variable having the distribution N(0,1).

Here are the steps for finding a Probability Corresponding to a normal Random variable.

1. Draw a normal curve first, do your best.
2. Next, label the center or mean of the curve with zero because standard normal curves have a mean of zero.
3. Put in scaling by finding the distance from the center to the inflection point. This distance above mu is one unit. Put in a 1, that is one standard deviation above mu.
4. Use Table IV in Appendix A to find the areas corresponding to the z-values.

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