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 $ 85,000. Suppose that 56% of the before-tax family incomes when the head of the household has a college degree are between $75,100 and $94,900 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?

Answer 1

Answer:

The mean before tax family income is $85,000.

56% of the before tax family incomes when the head of the household has a college degree are between $ 75,100 and $ 94,900 and these incomes are normally distributed.

Here we are given that

mean = 85,000

56% between 75,100 and 94900

Since , $ 85,000 is the mean , 50% is below 85,000

Percentage of income between $ 85,000 and 94,900

= 56 / 2

= 28%

P( income less than 94,900 ) = 28 +50

= 78 %

P(X< (94,900 - 75,100) / ) = 0.78

P( X < 19,800 / ) = 0.78

From stardard normal distribution table,

19,800 / = 0.78

= 25,384.615

The standard deviation of before tax family incomes when the head of the house hold has a college degree is 25384.615