What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $221 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals.

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The Wall Street Journal reported that 33% of taxpayers with adjusted gross income between $30,000 and $60,000 itemize to ductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $17,642. Assume that the standard deviation o =2050. Use z tables. 
a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $221 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals.

b. What is the average of a larger sample size one attempting to estimate the population mean? Rent your answers to four decimals.

A large sample increases the probability that the sample mean will be within a specified distance of the population mean. In this instance, the probability of being within+_221 of u ranges from ____ for a sample of size 32 ____ for a sample of size 40. 

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