# Alfred missed a class test. For the test that Alfred missed, the class mean was 18 and the standard deviation was 4. If his teacher is going to give Alfred a mark based on his standard score, what mark should Alfred receive?

## His teacher knows that Alfred usually scores 1.6 standard deviations above the class mean.

Jan 9, 2018

The teacher will give Alfred a score of $\textcolor{b l u e}{24.4}$.

#### Explanation:

Since his average z-score is 1.6 standard deviations above the class mean, the teacher has to convert that score into a number of points above the mean.

First, the teacher can multiply the standardized score by the standard deviation to find how many points above/below the mean, his score will be:
$1.6 \cdot 4 = 6.4$

Then, add this number to the mean to find his score:
$18 + 6.4 = 24.4$

The teacher will give Alfred a score of $\textcolor{b l u e}{24.4}$.