Question

A student is filling out a college application that requires she supply either her math SAT score or her math ACT score. She scored 610 on the math SAT and 27 on the math ACT. Which should she report given that the mean SAT math score was 515 with a standard deviation of 114, and the mean ACT math score was 21.0 with a standard deviation of 5.1

Answer 1

ACT

Explanation:

Answer 2

Due to the higher z-score, she should report her ACT grade.

Explanation:

Z-score:

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Which should she report

The grade with the higher z-score.

SAT:

Scored 610, mean 515, standard deviation 114. So
`X = 610, \mu = 515, \sigma = 114`

`Z = (X - \mu)/(\sigma)`

`Z = (610 - 515)/(114)`

`Z = 0.83`

ACT:

Scored 27, mean 21, standard deviation 5.1. So
`X = 27, \mu = 21, \sigma = 5.1`

`Z = (X - \mu)/(\sigma)`

`Z = (27 - 21)/(5.1)`

`Z = 1.18`

Due to the higher z-score, she should report her ACT grade.