Question

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 $ 84,800. Suppose that 62% of the before-tax family incomes when the head of the household has a college degree are between $74,900 and $94,700 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.)

Answer 1

Let ,

We have ,

............(I)

From standard normal distribution table , .................(II)

From (I) and (II) , we get ,

Therefore , the value of the standard deviation is $11250