You may need to use the appropriate appendix table or technology to answer this question.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 = $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: 30, 60, 100, and 400? (Round your answers to four decimal places.)

sample size n = 30

sample size n = 60

sample size n = 100

sample size n = 400

(b)What is the advantage of a larger sample size when attempting to estimate the population mean? choose one of option from below.

1)A larger sample lowers the population standard deviation.

2)A larger sample has a standard error that is closer to the population standard deviation.

3)A larger sample increases the probability that the sample mean will be within a specified distance of the population mean.

4)A larger sample increases the probability that the sample mean will be a specified distance away from the population mean.