According to the IRS, income tax returns one year averaged $1332 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 $1332, with a standard deviationof $725. Assume the amounts owed or due on tax returns are normally distributed.
a. what proportion of tax returns show a refund greater than $2000?
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 $100 and $700?
The solution file is attached.
= 1332, = 725, z = (x – )/
(a) z = (2000 – 1332)/725 = 0.92
P(x > 2000) …
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