Question

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 $2,200?
(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 $140 and $660?

(Round all the z values to 2 decimal places. Round your answers to 4 decimal places.)

(a) P(x > $2,200) =

(b) P(x < 0) =

(c) P($140 ≤ x ≤ $660) =

Answer 1

X: amount of refund for tax returns.

X~N(1332,725)

a).the proportion of tax returns show a refund greater than $2,200 be:-

[ from standard normal table]

b).the proportion of the tax returns show that the taxpayer owes money to the government be:-

[ from standard normal table]

c).the proportion of the tax returns show a refund between $140 and $660 be:-

[ from standard normal table]

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