In: Statistics and Probability
According to the Internal Revenue Service, income tax returns
one year averaged $1,332 in refunds for taxpayers. One explanation
of this figure is that taxpayers would rather have the government
keep back too much money during the year than to owe it money at
the end of the year. Suppose the average amount of tax at the end
of a year is a refund of $1,332, with a standard deviation of $725.
Assume that amounts owed or due on tax returns are normally
distributed.
(a) What proportion of tax returns show a refund
greater than $2,500?
(b) What proportion of the tax returns show that
the taxpayer owes money to the government?
(c) What proportion of the tax returns show a
refund between $150 and $680?
(Round all the z values to 2 decimal places. Round your
answers to 4 decimal places.)