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 $17,982. Assume that the standard deviation is = $2709. 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 $177 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals. n = 30 .7611 n = 50 .1788 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. the probability that the A larger sample decreases sample mean will be within a specified distance of the population mean. In this instance, the probability of being within 177 of ranges from 400. for a sample of size 30 to 3 for a sample of size