EXAMPLE 3 ACT versus SAT scores

Madison scored 600 on the SAT Mathematics exam. Her friend Gabriel took the American College Testing (ACT) test and scored 21 on the math part. ACT scores are Normally distributed with mean 18 and standard deviation 6. Assuming that both tests measure the same kind of ability, who has the higher score?

Madison’s standard score is

Compare this with Gabriel’s standard score, which is

Because Madison’s score is 1 standard deviation above the mean and Gabriel’s is only 0.5 standard deviation above the mean, Madison’s performance is better.