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The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100. Use z-table.
a. What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?

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Answer:

The CPA Practice Advisor

The probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean is:

= 56%

Explanation:

a) Data and Calculations:

Population mean (preparation fee for 2017 federal income tax returns) = $273

Population standard deviation of preparation fees = $100

Mean price for a sample of 30 federal income tax returns = $257 (which is within $16 of the population mean)

z = (x-μ)/σ

z = standard score

x = observed value

μ = mean of the sample

σ = standard deviation of the sample

Z = ($273 - $257)/$100

= 0.16

Using the z-table

P = 0.5636

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