The Wall Street Journal reported that 33% of taxpayers with adjusted gross incomes between $30,00 and $60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $16,573 . Assume that the standard deviation is $2148. Use z-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 $185 of the population mean for each of the following sample sizes: 30,50, 100, and 400? Round your answers to four decimals.