EXAMPLE 1.34 The NCAA Standard for SAT Scores

The National Collegiate Athletic Association (NCAA) requires Division I athletes to get a combined score of at least 820 on the SAT Mathematics and Verbal tests to compete in their first college year. (Higher scores are required for students with poor high school grades.) The scores of the 1.4 million students who took the SATs were approximately Normal with mean 1026 and standard deviation 209. What proportion of all students had SAT scores of at least 820?

Here is the calculation in pictures: the proportion of scores above 820 is the area under the curve to the right of 820. That’s the total area under the curve (which is always 1) minus the cumulative proportion up to 820.

47

That is, the proportion of all SAT takers who would be NCAA qualifiers is 0.8379, or about 84%.