The US department of labor posted the 2013 average salary fo

The US department of labor posted the 2013 average salary for grade 15 civilian employees who work for the federal government as $77,503. Assume annual salaries are normally distributed with standard deviation 6,550. Due to the economic downturn, managers at the top 3% of salaries will be asked to take a buyout package. Find the minimum salary targeted for buyout.

Solution

Top 3% means Upper limit of 94% Confidence interval

94% CI means z = 1.8808

z = (x-mean)/s.d

So 1.8808 = (x - 77503)/6550

So x = 75503 + (1.8808*6550) = 89820

So minimum salary targeted for buyout = $89,820