Question

On a nationwide math test, the mean was 63 and the standard deviation was 10. If Roberto scored 90, what was his z -score?

Answer 1

The z score is given by:

`\begin{gathered} z=(x-\mu)/(\sigma) \\ \text{ where:} \\ \mu\text{ is the mean} \\ \sigma\text{ is the standard deviation} \end{gathered}`

In this case the mean is 63, the standard deviation is 10 and Roberto's score is 90; plugging these values we have that:

`\begin{gathered} z=(90-63)/(10) \\ z=(27)/(10) \\ z=2.7 \end{gathered}`

Therefore, Roberto's z-score is 2.7