Bob made 116 on his accounting midterm and 82 on his biology midterm. For the accounting midterm, the mean score was 102 with standard deviation 14. For the biology midterm, the mean score was 70 with standard deviation of 5. Which score was the higher with respect to the rest of the class? Explain your answer

#### Solution

Let $X$ = Bob's score in accounting midterm

The $Z$ score formula is $Z= \dfrac{X-\mu}{\sigma}$.

For accounting midterm, the mean score was $\mu = 102$ and standard deviation was $\sigma =14$.

Bob's z score for accounting is

$Z= \frac{116-102}{14} = 1$.

Let $Y$ = Bob's score in biology midterm

The $Z$ score formula is $Z= \dfrac{Y-\mu}{\sigma}$.

For bilogy midterm, the mean score was $\mu = 70$ and standard deviation was $\sigma =5$.

Bob's z score for biology is

$Z= \frac{82-70}{5} = 2.4$.

Biology score is higher than accounting score with respect to the rest of the class, because the standard deviation of accounting score is high compare to biology score.