The Wall Street Journal reported that 33% of taxpayers with adjusted gross incomes between 30,000$ and 60,000$ itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was 16,041$ . Assume that the standard deviation is 2,264$. 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 155$ of the population mean for each of the following sample sizes: 30,50, 100,and 400? Round your answers to four decimals.

A larger sample increases the probability that the sample mean will be within a specified distance of the population mean. In the automobile insurance example, the probability of being within+ or - 155 of average ranges from ________ for a sample of size 30 to for____________ a sample of size of 400.