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 $16,278. Assume that the standard deviation is $2611. 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 $199 of the population mean for each of the following sample sizes: 30,50,100, and 400? Round your answers to four decimals.

b. What is the advantage of a larger sample size when attempting to estimate the population mean? 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 this instance, the probability of being within plus or minus 199 of ranges from _______ for a sample of size 30 to ______ for a sample of size 400.