Question

One year the ACT had a mean score of 21.2 and a standard deviation of 5.1. That same year, the SAT had a mean score of 1498 and a standard deviation of 347. Suppose that a scholarship committee is considering two students, one who scored 26 on the ACT and another who scored 1,800 on the SAT. Both are pretty good scores, but which one is better? Find the z-score for the ACT

Answer 1

ACT Score performed better.

Explanation:

Given :

ACT :

Mean score, μ = 21.2

Standard deviation, σ = 5.1

Score, x = 26

SAT :

Mean score, μ = 1498

Standard deviation, σ = 347

Score, x = 1800

To know which score is better, we obtain the standardized, Z score of the two examination :

Zscore = (x - μ) / σ

ACT Zscore :

(26 - 21.2) / 5.1

Zscore = 4.8 / 5.1 = 0.941

ACT Zscore = 0.941

SAT Zscore :

(1800 - 1498) / 347

Zscore = 302 / 347 = 0.870

SAT Zscore = 0.870

The student with the higher Zscore performed better :

ACT Zscore > SAT Zscore