The Wall Street Journal reported that 33% of taxpayers with adjusted oross incomes between 830,000 and $60,000 itemized deductions on their federal income tax retum. The mean amount of deductions for this population of taxpayers was $17,338. Assume that the standard deviation is =$2447. 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=30n=50n=100n=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 samplel 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 400 . for a sample of size 30 to for a sample of size