Statistics 6.1: Normal Distribution

This isn't a rule, but...

In the case that you're asked to find the area of two shaded places on the ends of the curve... For example, #25 on p. 312, you would basically find the areas separately and then once you have both of them, you add them together. Just look at how you did it in the homework for 6.1 #25

Rule #3

To find the *area between any two z-values*, you *look up the z-values* in Table E and then *subtract the smaller area from the larger area*.

What are the properties of a normal distribution?

1. The *mean, median, and mode are all equal*, and they are *located at the center* of the distribution. 2. The distribution is *unimodal* (has only one mode). 3. The curve *never touches the x axis*. 4. The distribution is *symmetric* about the mean. In other words, if you were to draw a line down towards the mean, both sides would be the same mirror images of each other. 5. The area (*space under the curve is = to 1*) under the curve is one.

Normal Distribution

A continuous, bell-shaped distribution of a random variable x. For example, grades are supposed to follow normal distribution. You would hope for a C average.

Standard Normal Distribution

A normal distribution in which the *mean is 0* and the *standard deviation is 1*. All values on the horizontal axis are called z-values.

Rule #1

To find the area to the *left* of any z-value, *look up the z-value in Table E to find the area*.

Rule #2

To find the area to the *right* of any z-value, *look up the z-value* in Table E, and *then subtract the area from 1*. To remember: "It is right to remember that you must subtract 1 from the area!"