Question

Consider that ages of professors in a community college are normally distributed with a mean of 48.5 and standard deviation of 12.4. What percentage of the professor are younger than 40?

Answer 1

SOLUTIONS

A community college are normally distributed with a mean of

48.5 and a standard deviation of 12.4.

$Z_{score}=\frac{x-\mu}{\sigma}$$\begin{gathered} x=40 \\ \mu=48.5 \\ \sigma=12.4 \end{gathered}$$Z_{score}=\frac{40-48.5}{12.4}=-0.685$

Therefore the percentage of the professor younger than 40 is

P(x<40) = 0.24652

$0.24652\text{ }\times100=24.65\text{\%}$

Answer = 24.65%