Question

1. three students take equivalent stress tests. which is the highest relative score (meaning which has the largest z - score value)?

a. a score of 144 on a test with a mean of 128 and a standard deviation of 34.
b. a score of 90 on a test with a mean of 86 and a standard deviation of 18.

Explanation:

Step1: Recall z - score formula

$z=\frac{x - \mu}{\sigma}$

Step2: Calculate z - score for a

$z_a=\frac{144 - 128}{34}=\frac{16}{34}\approx0.47$

Step3: Calculate z - score for b

$z_b=\frac{90 - 86}{18}=\frac{4}{18}\approx0.22$

Answer:

The largest z - score is for a with $z\approx0.47$