Question

When given a raw score, explain how to use the normal curve to compare that

Answer 1

First of all, you need to come to an understanding of what you mean by "compare that score to the population." Often, that will mean determining the percentile rank of the score.

To determine the percentile rank of a raw score, you first nomalize it by determining the number of standard deviations it lies from the mean. That is, you subtract the population mean and divide that difference by the population standard deviation. Now, you have what is referred to as a "z-score".

Using a table of standard normal probability functions (or an equivalent calculator or app), you look up the cumulative distribution value corresponding to the z-score you have. This number between 0 and 1 (0% and 100%) will be the percentile rank of the score, the fraction of the population that has raw scores below the raw score you started with.