According to the Internal Revenue Service, income tax returns oneyear averaged $

Question

According to the Internal Revenue Service, income tax returns oneyear averaged $1,332 in refunds for taxpayers. One explanation ofthis figure is that taxpayers would rather have the government keepback too much money during the year than to owe it money at the endof the year. Suppose the average amount of tax at the end of a yearis a refund of $1,332, with a standard deviation of $725. Assumethat amounts owed or due on tax returns are normallydistributed.

(a) What proportion of tax returns show a refund greaterthan $2,000?

(b) What proportion of the tax returns show that thetaxpayer owes money to the government?

(c) What proportion of the tax returns show a refundbetween $100 and $700?

Explanation / Answer

Given X~Normal(=1332, =725) (a) P(X>2000)=P((X-)/ > (2000-1332)/725) =P(Z>0.92) =0.1788 (17.88%) (check normal table) ------------------------------------------------------------------------------- (b) P(X

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