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 o = $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, 50, 100, and 500? (Round your answers to four decimal places.) sample size n = 30 sample size n = 50 sample size n = 100 sample size n = 500 (b) What is the advantage of a larger sample size when attempting to estimate the population mean? A larger sample has a standard error that is closer to the population standard deviation, A larger sample increases the probability that the sample mean will be a specified distance away from the population mean, A larger sample increases the probability that the sample mean will be within a specified distance of the population mean. O A larger sample lowers the population standard deviation