Question

Raul received a score of 75 on a history test for which the class mean was 70 with a standard deviation of 8. He received a score of 80 on a biology test for which the class mean was 70 with standard deviation 5. On which test did he do better relative to the rest of the class

Answer 1

Raul did better in biology test relative to the rest of the class.

Explanation:

We are given two situations;

• Raul received a score of 75 on a history test for which the class mean was 70 with a standard deviation of 8.

• He received a score of 80 on a biology test for which the class mean was 70 with standard deviation 5.

Now, we have to find on which test did he do better relative to the rest of the class. For this we will calculate z score for both the situations;

The z score value is given by, Z =
`(X-\mu)/(\sigma)` ; where,
`\mu` = mean

`\sigma` = standard deviation

For 1st situation; z score =
`(75 -70)/(8)` = 0.625

For 2nd situation; z score =
`(80 -70)/(5)` = 2

So, it is clear that 2nd situation is better as it has higher z score.

Therefore, Raul did better in biology test relative to the rest of the class.