Consider an economy with a flat rate tax system. Each dollar of income over $5000 is taxed at 20%. (Income below $5000 is tax free.) In general, T = .2(Y − 5000) = −1000 + .2Y, where T is taxes and Y is income. Suppose that the population mean income is $20,000 and that the population standard deviation of incomes is $8000. All families have at least $5000 of income.
a. find the mean of T.
b. Find the standard deviation of T.
c. If the population contains 20 million families, what is the government’s total tax revenue.