SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8 and a standard deviation of 4.8. A student takes both tests while a junior and scores 1130 on the SAT and 25 on the
ACT. Compare the scores.
A)A score of 25 on the ACT test was better.
B)A score of 1130 on the SAT test was better.
C)The two scores are statistically the same.
D)You cannot determine which score is better from the given information.

Question

Quizplus · Accepted Answer

To compare the scores, we convert them to z-scores. For the SAT: $z = \frac{1130 - 1026}{209} \approx 0.497$. For the ACT: $z = \frac{25 - 20.8}{4.8} \approx 0.875$. A higher z-score indicates a score further above the mean, so the ACT score is better.

SAT Scores Have a Mean of 1026 and a Standard