Question

A friend tells you about a recent study dealing with the number of years of teaching experience among current college professors. He remembers the mean but cannot recall whether the standard deviation was 6​ months, 6​ years, or 16 years. Tell him which one it must have​ been, and why.

Answer 1

From the normal distribution, we know that 98.7% of observations will fall within 3 standard deviations of the mean. If you assume it is 6 months, 3 SDs above the mean would be 6*3=18 months, and due to symmetry, 18 months below the mean. Does it make sense that 98.7% of college professors have taught for time periods which all fall within 36 months of each other? I don't think so, it has to be more varied than this. How about within 36 years (assuming SD=6 years)? That seems more reasonable. It has to be 6 years.