Question

Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with mean 554 and standard deviation 106. Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with mean 24.7 and standard deviation 3.2.

1. What is Elanor's standardized score?
Round to 2 decimal places.
2. What is Gerald's standardized score?
Round to 2 decimal places.
3. Assuming that both tests measure the same kind of ability, who has the higher score?
a. Gerald.
b. Elanor.
c. They both did equally well.

Answer 1

1. Elanor's standardized score is 1.19
2. Gerald's standardized score is 0.72
3. Elanor has higher score

Explanation:

To compare Elanor's and Gerald's math scores, we need to standardize them and calculate their z-scores.

z score can be calculated using the formula

z=
`(X-M)/(s)` where

• X is the student's score

• M is the mean score of the exam

• s is the standard deviation of the exam

Elanor's standardized score is:

z(e) =
`(680-554)/(106)` ≈ 1.19

Gerald's standardized score is:

z(g)=
`(27-24.7)/(3.2)` ≈ 0.72

Since z(e) > z(g), Elanor has higher score