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 wall street journal, october 25, 2012). the mean amount of deductions for this population of taxpayers was $16,642. assume the standard deviation is σ = $2400 .
a. what is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean for each of the following sample sizes: 30, 50, 100, and 400?
b. what is the advantage of a large sample size when attempting to estimate the population mean?