Question

A student scores 74 on a geography test and 273 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 5 mathematics test has a mean of 300 and a standard deviation of 18. If the data for both tests are normally distributed, on which test did the stu score better relative to the other students in each class? A. The student scored better on the geography test. B. The student scored the same on both tests.C. The student scored better on the mathematics test

Answer 1

A. The student scored better on the geography test.

Explanation:

The z-score for a normal distribution, for any value X, is given by:

`z=(X-\mu)/(\sigma)`

Where is μ the mean score, and σ is the standard deviation.

For the Geography test:

X = 74

μ = 80

σ = 5

`z_g=(74-80)/(5)\\ z_g=-1.2`

For the Mathematics test:

X = 273

μ = 300

σ = 18

`z_m=(273-300)/(18)\\ z_m=-1.5`

The z-score for the Geography test is higher than the score for the Mathematics test, which means that the student had a better relative score in the Geography test.

The answer is A. The student scored better on the geography test.