Question

A good use of z-scores is to compare values in two different distributions. Suppose your instructor will drop the low test when computing final grades, but he curves grades on each test. You had a 92 on the first test, and an 85 on the second. The first test had a mean of 83 and standard deviation of 6. The second test had a mean of 75 and standard deviation 3. The test with the relatively better score is ____________.

Answer 1

The Second Test has a relatively better score with a Z-Score of 3.33 as compared with a Z-Score of 1.5 from the First Test.

Explanation:

The formula for calculating a Z-Score is z = (x – μ) / σ

x represents the Test Score

μ represents the mean for the test

σ represents the Standard Deviation for the test

Z score for Test 1

(92-83)/6= 1.5

Z Score for Test 2

(85-75)/3= 3.33

The Z Score of 3.33