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The Wall Street Journal reported that 33% of taxpayers with adjusted gross incomes between $30,000 and...

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Basic Math

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 $15,968. Assumethat the standard deviation is $2,190. Use z-table.

a. What is the probability that a sample oftaxpayers from this income group who have itemized deductions willshow a sample mean within $184 of the population mean for each ofthe following sample sizes: 30, 50, 100, and 400? Round youranswers to four decimals.

b. What is the advantage of a larger samplesize when attempting to estimate the population mean? Round youranswers to four decimals.

A larger sample (Select your answer -increasesor decreases) the probability that the sample meanwill be within a specified distance of the population mean. In theautomobile insurance example, the probability of being within+/-184 of u ranges from (blank) for a sample ofsize 30, to (blank) for a sample of size 400.

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