Question

A student took two national aptitude tests. The national mean and standard deviation were 325 and 100, respectively, for the first test, and 50 and 6, respectively, for the second test. The student scored 425 on the first test and 65 on the second test. Use z-scores to determine on which exam the student performed better relative to the other test takers. first exam

Answer 1

Second test

Explanation:

Given that :

FIRST TEST

Mean (m) = 325

Standard deviation (s) = 100

Score (x) = 425

SECOND TEST

Mean (m) = 50

Standard deviation (s) = 6

Score (x) = 65

Express both scores as standardized scores:

Zscore = (x - m) / s

First Score :

Zscore = (425 - 325) / 100

Zscore = 100/100 = 1

SECOND SCORE :

Zscore = (65 - 50) / 6

Zscore = 15 / 6 = 2.5

Student performed better on second test :

Zscore second > Zscore first