Checkpoint: z-Scores Solution

The technology supervisor determined that $\mu =11, \sigma =2$, for the number of emails received each day by teachers at Fair View High School.

1. What proportion of teachers received fewer than eight emails in one day?
2. How many emails will a teacher receive in the 85th percentile?

1. $$\begin{gathered} z=\frac{8–11}{2}=–1.5 \\ \mathrm{P}(\mathrm{emails}<8)=0.0668 \end{gathered}$$

Note

Q: How many emails will 50% of teachers receive? Explain.


A: 50% of teachers will receive 11 emails or fewer because 11 is the mean.