The Federal Reserve System publishes data on family income b

The Federal Reserve System publishes data on family income based on its Survey of Consumer Finances. When the head of the household has a college degree, the mean before-tax family income is $ 84,900. Suppose that 54% of the before-tax family incomes when the head of the household has a college degree are between $75,200 and $94,600 and that these incomes are normally distributed. What is the standard deviation of before-tax family incomes when the head of the household has a college degree?

(Round the value of z to 2 decimal places. Round your answer to 2 decimal places.)

Solution

If 52% is in the middle, 1 - .52 = .48 is in the ends, .24 in each end.

Z score at .24 = -.71

X = z*sd + mean

74,600 = -.71*sd + 84,850

-10,250 = -.71*sd

Standard deviation = 14436.92