The Wall Street Journal reported that 33% of taxpayerswith adjusted gross incomes between $30,000 and $60,000 itemizeddeductions on their federal income tax return. The mean amount ofdeductions for this population of taxpayers was $16,928 . Assumethat the standard deviation is $2,903.
(a) What is the probability that a sample of taxpayers from thisincome group who have itemized deductions will show a sample meanwithin $151 of the population mean for each of the following samplesizes: 30, 50, 100, and 400? Round your answers to fourdecimals.
(b) What is the advantage of a larger sample size whenattempting to estimate the population mean? Round your answers tofour decimals.
A larger sample increases the probability that the sample meanwill be within a specified distance of the population mean. In theautomobile insurance example, the probability of being within(plus/minus) $151 of m ranges from (blank) for a sample of size 30to (blank) for a sample of size 400.
