Question

Scores on the ACT exam have a N(μ = 18,σ = 6) distribution, while scores on the SAT

exam have a N(μ = 500,σ = 100) distribution. Suppose Xiaoyu got a 27 on the ACT
exam, while Emily got a 720 on the SAT exam. Who has the higher relative score? Why?

Answer 1

Emily has a higher relative score since her z-score is higher. This would mean she scored further above the mean than Xiaoyu.

Explanation:

Find the z-scores by subtracting the score they got by the mean and then dividing by the standard deivation of their respective exams.

Xiaoyu:

z =
`(27 - 18)/(6)` = 1.5

Emily:

z =
`(720 - 500)/(100)` = 2.2

______

Emily has a higher relative score since her z-score is higher. This would mean she scored further above the mean than Xiaoyu.