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)=(x-\mu)/(\sigma)`
`\begin{gathered} x=40 \\ \mu=48.5 \\ \sigma=12.4 \end{gathered}`
`Z_(score)=(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{ }*100=24.65\text{\%}`

Answer = 24.65%