Q. 3.27

Test Scores

A student scored 85 on an English test while the mean score of all the students was 76 and the standard deviation was 4. She also scored 42 on a French test where the class mean was 36 and the standard deviation was 3. Compare the relative positions on the two tests.

Verified Solution

First find the $\mathrm{z}$ scores. For the English test

$z=\frac{X-\bar{X}}{s}=\frac{85-76}{4}=2.25$

For the French test

$z=\frac{X-\bar{X}}{s}=\frac{42-36}{3}=2.00$

Since the z score for the English test is higher than the z score for the French test, her relative position in the English class is higher than her relative position in the French class.