Standard Normal Distribution

Question

The average salary for graduates entering the teaching field is $40,000. If 11.5% of graduates entering the teaching field earn more than $46,000, find the standard deviation. Assume the salaries are normally distributed.

Answer 1

First, we need to find the z-score that corresponds or closely corresponds to 11.5% or 0.115. We see that 0.115 is closest to the z-score of -1.20. Now compare that to positive 1.20 and you'll see that 88.5% of the teachers earned less than $46000. To keep things positive, we will use the positive z-score

So, given the z-score, we can now manipulate the z-score formula to find our standard deviation

z = (x-mean)/sd

becomes sd = (x-mean)/z-score

So, sd = (46000 - 40000) / 1.2 = 6000 / 1.2 = 5000

So your standard deviation will be $5,000