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 0' = $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 follo sample sizes: 30, 50, 150, and 400? (Round your answers to four decimal places.) sample size n = 30 0.3472 sample size n = 50 0.4380 sample size n = 150 .6922 X'XX sample size n = 400 0.9030 (b) What is the advantage of a larger sample size when attempting to estimate the population mean? O A larger sample increases the probability that the sample mean will be a specied distance away from the population mean. 0 A larger sample has a standard error that is closer to the population standard deviation. 0 A larger sample lowers the population standard deviation. (Q A larger sample increases the probability that the sample mean will be within a specied distance of the population mean