The Wall Street Journal reports 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 $16,642. Assume the standard deviation is σ = $2,400.

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: 20, 50, 100, and 500?
b). What is the advantage of larger sample size when attempting to estimate the population means?

a). A larger sample increases the probability that the sample mean will be a specified distance away from the population mean.
b). A larger sample increases the probability that the sample mean will be within a specified distance of the population mean.    
c). A larger sample lowers the population standard deviation.
d). A larger sample has a standard error that is closer to the population standard deviation.