A student scores 62 on a geography test and 282 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 15. The mathematics test has a mean of 300 and a standard deviation of 12. 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 mathematics test.
B) The student scored the same on both tests.
C) The student scored better on the geography test.

Question

Quizplus · Accepted Answer

The student's score relative to others can be determined by calculating the z-score for each test. The z-score is calculated as (score - mean) / standard deviation. For the geography test, the z-score is (62 - 80) / 15 = -1.2. For the mathematics test, the z-score is (282 - 300) / 12 = -1.5. A higher z-score indicates a better relative performance, so since -1.2 is higher than -1.5, the student scored better on the geography test relative to others.

A Student Scores 62 on a Geography Test and 282