Question

You have the responsibility of reviewing students who apply to your University and helping choose the most qualified applicants. Some students took the ACT and some took the SAT. You want to compare two students. Student A took the ACT and got a score of 24, while student B got an SAT score of 1100. The year they took their tests, the ACT had an average score of 20.8 and a standard deviation of 5.6, while the SAT had an average score of 1060 and standard deviation of 195. Looking at just these test scores, which student appears more qualified?

Answer 1

Student who took ACT appears to be more qualified.

Explanation:

We are given that Student A took the ACT and got a score of 24, while student B got an SAT score of 1100.

The year they took their tests, the ACT had an average score of 20.8 and a standard deviation of 5.6, while the SAT had an average score of 1060 and standard deviation of 195.

We have to check which student appears more qualified.

We will do this by finding the z scores for both the students and the student with higher z score is considered to be more qualified.

The z score probability distribution for a normal distribution is given by;

Z =
`(X-\mu)/(\sigma)` ~ N(0,1)

where,
`\mu` = average score

`\sigma` = standard deviation

Let X = score of the student

• Student z score who took the ACT is given by;

For this student : X = score of ACT = 24

`\mu` = average score for ACT = 20.8

`\sigma` = standard deviation for ACT = 5.6

So, z score =
`(X-\mu)/(\sigma)`

=
`(24-20.8)/(5.6)` = 0.571

Hence, the student who took ACT has a z score of 0.571.

• Student z score who took the SAT is given by;

For this student : X = score of SAT = 1100

`\mu` = average score for SAT = 1060

`\sigma` = standard deviation for SAT = 195

So, z score =
`(X-\mu)/(\sigma)`

=
`(1100-1060)/(195)` = 0.205

Hence, the student who took SAT has a z score of 0.205.

Therefore, it is clear that the z score for ACT is higher than that of SAT which means that student who took ACT appears to be more qualified.