EXAMPLE 5 Finding the observation that matches a percentile

How high must a student score on the SAT to fall in the top 10% of all scores? That requires a score at or above the 90th percentile. Look in the body of Table B for the percentiles closest to 90. You see that standard score 1.2 is the 88.49 percentile and standard score 1.3 is the 90.32 percentile. The percentile in the table closest to 90 is 90.32, so we conclude that a standard score of 1.3 is approximately the 90th percentile of any Normal distribution.

To go from the standard score back to the scale of SAT scores, “undo” the standard score calculation as follows:

observation = mean + standard score × standard deviation

= 500 + (1.3)(100) = 630

A score of 630 or higher will be in the top 10%. (More exactly, these scores are in the top 9.68% because 630 is exactly the 90.32 percentile.)