Provide an appropriate response.
-For the mathematics part of the SAT the mean is 514 with a standard deviation of 113, and for the mathematics part of the ACT the mean is 20.6 with a standard deviation of 5.1. Bob scores a 660 on the SAT and a 27 on the
ACT. Use z-scores to determine on which test he performed better.
A)SAT
B)ACT

Question

Quizplus · Accepted Answer

To determine on which test Bob performed better, we need to compare his z-scores for each test.

For the SAT: 
z-score = (660-514)/113 = 1.29

For the ACT: 
z-score = (27-20.6)/5.1 = 1.26

Both z-scores indicate that Bob performed above the average for each respective test. However, since his z-score is slightly higher for the SAT, we can conclude that he performed better on the SAT. To compare Bob's performance, we need to compute his z-scores for both tests.

For the SAT:

z = (660-514)/113 = 1.29

For the ACT:

z = (27-20.6)/5.1 = 1.25

Since z-scores reflect the number of standard deviations above or below the mean, we can see that Bob performed better relative to his peers on the SAT, where he scored 1.29 standard deviations above the mean, compared to 1.25 on the ACT. Therefore, the best choice is A: SAT.

Provide an Appropriate Response