Question

Raul received a score of 80 on a history test for which the class mean was 70 with standard deviation 10. He received a score of 75 on a biology test for which the class mean was 70 with standard deviation 2.5. On which test did he do better relative to the rest of the class?

Answer 1

Answer:

Raul performed better in the biology test

Step-by-step explanation:

Given

History

$Score = 80$

$Mean = 70$

$Standard\ Deviation = 10$

Biology

$Score = 75$

$Mean = 70$

$Standard\ Deviation = 2.5$

Required

Where did he perform better relative to other students

To do this, we simply calculate the z score in both tests and make comparison.

z score is calculated as thus;

$z = \frac{x - Mean}{SD}$

For history;

$z = \frac{80 - 70}{10}$

$z = \frac{10}{10}$

$z = 1$

For biology;

$z = \frac{75 - 70}{2.5}$

$z = \frac{5}{2.5}$

$z = 2$

Since the z score in the biology test is greater than that of the history test, then he performed better in the biology test