Question

The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. what is the probability that a randomly selected teacher earns more than $525 a week?
your answer should be a decimal rounded to the fourth decimal place.

Answer 1

The probability is 0.2177.

The z-score associated with this income is

z = (525-490)/45 = 0.78

Using a z-table (http://www.z-table.com) we see that the area to the left of this score, less than the score, is 0.7823.  We want the probability greater than this score, so we subtract from 1:
1 - 0.7823 = 0.2177.