The Wall Street Journalreported that33%of taxpayers with adjusted gross incomes between $30,000and$60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $16,973. Assume that the standard deviation is $248. 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 withinof the population mean for each of the following sample sizes: 30,50,100, 400 and? Round your answers to four decimals.