Determine and Interpret z-Scores
-A student scores 74 on a geography test and 243 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 5. The mathematics test has a mean of 300 and a standard deviation of 38. If the data for both tests are normally distributed, on which test did the student score better relative to the other students in each class
A) The student scored better on the geography test.
B) The student scored better on the mathematics test.
C) The student scored the same on both tests.

Question

Quizplus · Accepted Answer

To determine on which test the student scored better relative to others, we calculate the z-scores for both tests. For the geography test: $z = \frac{74 - 80}{5} = -1.2$. For the mathematics test: $z = \frac{243 - 300}{38} = -1.5$. A z-score closer to 0 indicates a score closer to the mean, so a z-score of -1.2 (geography) is better than -1.5 (mathematics), indicating the student scored relatively better on the geography test.

Determine and Interpret Z-Scores