Question

The age of professors at GHC is normally distributed with a mean of 42 years and a standard deviation of 5 years. A 30-year-old professor represents how many standard deviations from the mean? Find the number of standard deviations, and the direction.

Answer 1

$30=42+5x\implies 5x=-12\implies x=-\dfrac{12}5=-2.4$

So a 30 year old professor would be 2.4 standard deviations less than the mean.