In 1982 Abby’s mother scored at the 93rd percentile in the math SAT exam. In 1982 the mean score was 503 and the variance of the scores was 9604. In 2008 Abby took the math SAT and got the same numerical score as her mother had received 26 years before. In 2008 the mean score was 521 and the variance of the scores was 10,201. Math SAT scores are normally distributed and stated in multiples of ten.
Calculate the percentile for Abby’s score.
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Solution: B
From the table the 93rd percentile comes from a z-score between 1.47 and 1.56. 1.47 implies a test score of 503 + 1.47(98) = 647.1. Similarly, 1.56 implies a score of 655.9. The only multiple of 10 in this range is 650. Abby’s z-score is then (650 – 521)/101 = 1.277. This is at the 90th percentile of the standard normal distribution.
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.