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.

We can use the z-scores to directly compare the relative positions of each test.

Z-Score for the English test:

\[z=\frac{x-\overline{x}}{s}=\frac{85-76}{4}= 2.25\]

Z-Score for the French test:

\[z=\frac{x-\overline{x}}{s}=\frac{42-36}{3}=2.00\]

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.