Statistics with standard deviation and mean

Question

According to an article the average salary of Actuaries in the US is $98,620 a year. Suppose that currently the distribution of annual salary of all or actuaries is the US is approximately a normal with a mean of $98,620 in a standard deviation of $18,000. How much would an actuary have to be paid in order to be in the highest paid 10% of all actuaries?

Answer 1

Obtain a z-score chart

http://www.utdallas.edu/dept/abp/zscoretable.pdf

 

The z-score for 90% is 1.283 (interpolated)

 

1.283 = (X - 98620) / 18000         multiply both sides by 18000

23094 = X - 98620                       add 98620 to both sides

121714 = X

 

To be in the top 10% the salary must be greater than or equal to $121,714.