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 $15, 999 . Assume that the standard deviation is σ=$2262. Use z-table. a. What is the probebility that a sample of taxpayers from this income group who hove itemized deductions will show a sample mean within $224 of the population mean for each of the following sample sizes: 30,50,100, and 400? Round your answers to four decimals. n=30
n=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 the probability that the sample mean will be within a specined distance of the population mean, In this instance, the probablity of being within ±224 of μ ranges from _____ for a sample of size 30 to _____ a sample of size 400 ,