Standard deviation

Question

Teacher’s salaries in Georgia are normally distributed with an average salary of $52,000 with a standard deviation of $12,000. What percentage of teachers earn an a salary between $40,000 and $76,000?

Answer 1

In this case, all the data you are interested in lies between -1 standard deviation and +2 standard deviations.

In a normal distribution, between the mean and 1 standard deviation, there is 34.1% of the population so between ± 1 standard deviation, there is 68.2% of the population. Between 1 standard deviation and 2 standard deviations, there is 13.6% of the population. Like this:

Based on this:

The percentage of teachers that earn between $40,000 and $52,000 is 34.1%

The percentage of teachers that earn between $52,000 and $64,000 is 34.1%

The percentage of teachers that earn between $64,000 and $76,000 is 13.6%

So the total percentage of teachers that earn between $40,000 and $76,000 is 34.1 + 34.1 + 13.6 = 81.8%