Assume that the average annual salary for a worker in the United States is $32,000 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $7,000. Find the following:

Question

Assume that the average annual salary for a worker in the United States is $32,000 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 $24,000? 
(B)  What percentage of Americans earn above $36,000? 
 
Please show all of your work.
  (Points : 6)

drwls · Answer

(A) 24,000 is 8/7 of one standard deviation below the mean.

(B) 36,000 is 4/7 of one standard deviation above the mean.

You need a "normal distribution" table or computational tool to compute the percentages below 24,000 and above 36,000.

There is one such calcualtor tool at
http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html

For (A), I get 12.65%
For (B), I get 28.4%