Question

Assume that the average annual salary for a worker in the United States is 300,000- and that the annual salaries For Americans are normally distributed with a standard deviation equal to $7,000. Find the following:
A. What percentage of Americans earn below $22,000?
B. What percentage of Americans earn above 42,000?

Answer 1

I'm going to assume that you mean the average annual salary is $30k, not $300k - because $300k sounds a bit excessive to me, even for Americans! If so, the proportion of Americans who earn below $22k should be the area to the left of ($22k-$30k)/$7k = -1.143 in a set of Normal tables, which is 12.7%. The same sort of calculation for b) gives the area to the right of ($42k-$30k)/$7k = 1.714, which is the same as 1 - (area to the left of 1.714) = 1 - 0.957 = 4.3%.