The Wallf 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 $15,795. Assume that the standard deviation is 0' = $2204. 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 $186 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals. n=30 \"=50 n=lOO 112400 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 the probability that the sample mean will be within a specied distance of the population mean. In this instance, the probability of being within $186 of ,u ranges from for a sample of size 30 to for a sample of size 400