The Wall Street Journa, reported that 33% of taxpayers with a usted gross income

Question

The Wall Street Journa, reported that 33% of taxpayers with a usted gross incomes between 830,000 and $60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was S 17,630. Assume that the standard deviation is $2,069 usez table. 7. a.What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $179 of the 10C o population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals 30 n50 100 400 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 sampleSelect your answer 3 the probability that the sample mean will be within a specified distance of the population mean. In the automobile insurance example, the probability of being within t179 of u ranges from for a sample of size 30 to for a sample of size 400.

Explanation / Answer

here for n=30;

therefore from above:

b)

ranges from 0.2866 for a sample of size 30 to 0.8202 for a sample of size 400.

for normal distribution z score =(X-)/ here mean=       = 17630 std deviation   == 2669.000 sample size       =n= 30 std error=x=/n= 487.2905

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