For the year 2010, 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 $16,642. Assume that the standard deviation is σ = $2,240. If required, round your answer to two decimal places.

a) What is the probability that the sample of taxpayers from his income group who have itemized deductions will show a simple mean within $200 of the population mean for each of the following sample sizes:30, 50, 100 and 400?
b) What is the advantages of a larger sample size when attempting to estimate the population mean?