Question

when given a raw score, explain how to use the normal curve to compare that score to the population.

I don't really understand this question and how to answer.

Answer 1

It depends on a lot of assumptions. IF we assume the population of scores is Normally distributed, AND we know the population mean and standard deviation, then we can tell where our particular individual's raw score falls on that distribution.

Say, for example, the mean SAT score is 500 and the standard deviation is 100 (this is how the scores are actually scaled, by the way!). Our student scores a 650 on the SAT. We know that is 1.5 standard deviations above the mean of the population.

You could also translate that to a percentile if you wanted to. The mean of a Normal distribution is the 50th percentile. The area under the curve from -infinity to +1.5 standard deviations would be the proportion of cases with a 650 or less in the population - multiply that proportion by 100 to get a percentile.