Question

A student scores 62 on a geography test and 261 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 26. 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?

The Z-score for the student's geography test is _____
The Z-score for the student's math test is _____
Since the higher Z-score is the ______ test the_____ test is better relative to other
students in that class.

Answer 1

To determine on which test the student scored better relative to other students, we need to calculate the Z-scores. A higher Z-score indicates a better score relative to other students in the class.

Step-by-step explanation:

To determine on which test the student scored better relative to other students in each class, we need to calculate the Z-scores. The Z-score of a data point represents how many standard deviations it is away from the mean. A higher Z-score indicates a better score relative to other students in the class.

For the geography test:

Z-score = (Score - Mean) / Standard Deviation = (62 - 80) / 15 = -1.2

For the mathematics test:

Z-score = (Score - Mean) / Standard Deviation = (261 - 300) / 26 = -1.5

Since the Z-score for the math test (-1.5) is lower than the Z-score for the geography test (-1.2), the student scored better relative to other students in the geography class.