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 = $2,440. If required, round your answer to two decimal places.
(a) What are the sampling distributions of x for itemized deductions for this population of taxpayers for each of the following sample sizes: 30, 50, 100, and 400?
(b) What is the advantage of a larger sample size when attempting to estimate the population mean?