Click on the following links - please note these will open in a new window
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?
Enter the quantities above into their respective cells on the page in front of you. Once you have done so, hit the return key on your keyboard. The associated z-score is 0.4. At the bottom of the box you are working in, use the dropdown menu to select "Cumulative." Since the area under the curve is 0.655, we can easily see from the graph that that this score serves as the 65.5th percentile, meaning that about 35% of scores fall above this particular score and about 65% of scores fall below it.
Repeat the above example on your own. Be sure to consider raw scores that are both above and below the mean score. In comparing the results for scores above and below the mean, how do the Z scores differ? How do the areas under the normal curve differ?