Question

Raul received a score of 71 on a history test for which the class mean was 70 with a standard deviation of 5. He received a score of 74 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?

biology test

history test    

the same

Answer 1

For any random Variable X with mean $\mu$ and standard deviation $\sigma$ , the z score is given by

Z score = $\frac{X-\mu}{\sigma}$

For history test,

Mean = 70 , standard deviation = 5

For score 71 , z score = $\frac{71-70}{5}$ = 0.2

For biology test ,

Mean = 70 , standard deviation= 5

For score 74, Z score = $\frac{74-70}{5}$ = 0.8

Clearly z score is higher in Biology test than History test.

This indicates he scores better in Biology test .

In biology test he did better relative to the rest of the class .