6.9 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 taxpayer 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 $2,000? 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?

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6.9 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 $2,000?
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?
Transcribed Image Text:6.9 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 $2,000? 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?
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