The Wall Street Journalreported that33% of taxpayers with adjusted gross incomes between$30,000and $60.000itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $17,559. Assume that the standard deviation is $2,111. Usez-table.

a.What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within$235of the population mean for each of the following sample sizes:30, 50, 100 and400

? Round your answers to four decimals.

n=30

n=50

n=100

n=400

b.What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four decimals.

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