Begin by watching the following illustration of the normal distribution: http://www.ms.uky.edu/~mai/java/stat/GaltonMachine.html

Next, navigate to the following URL: http://psych-www.colorado.edu/~mcclella/java/normal/normz.html

Using the tools provided on this Web page, we can enter an observed value (see "Y"), the sample mean (see "Mean"), and the sample standard deviation (see "Std Dev") and automatically have the Z score and the area under the normal curve calculated for us. Let's try an example.

When the Scholastic Aptitude Test, later renamed the Scholastic Assessment Test (SAT), was first developed, scoring was originally designed to result in a mean of 500 per section, with a standard deviation of 100. Suppose that a student obtains a 540 on the math section of the test. What is the associated Z score? What is the associated area under the normal curve?