The Wall Street Journal reported 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 $17,983. Assume that the standard deviation is = $2114. Use z-table. a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $165 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals. n = 30 71=50 n = 100 n = 400 b. What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four decimals. A larger sample - Select your answer the probability that the sample mean will be within a specified distance. of the population mean. In this instance, the probability of being within 165 of ranges from sample of size 30 to for a sample of size 400. for a