EXAMPLE 4 Percentiles for college entrance exams

Madison’s score of 600 on the SAT translates into a standard score of 1.0. We saw that the 68–95–99.7 rule says that this is the 84th percentile. Table B is a bit more precise: it says that standard score 1 is the 84.13 percentile of a Normal distribution. Gabriel’s 21 on the ACT is a standard score of 0.5. Table B says that this is the 69.15 percentile. Gabriel did well, but not as well as Madison. The percentile is easier to understand than either the raw score or the standard score. That’s why reports of exams such as the SAT usually give both the score and the percentile.