An auditor for the Internal Revenue Service (IRS) is testing new fraud detection

Question

An auditor for the Internal Revenue Service (IRS) is testing new fraud detection software that regularly selects random samples of 100 individual tax returns from the previous year and examines the average calculated tax refund. Assuming that in the previous year, the distribution of tax returns was normal with a true mean of $1,350 and a standard deviation of $700, what is the probability that, in a random sample of 100 returns, the sample mean refund would be greater than $1500? Hint: this is a sampling distribution problem.

Explanation / Answer

Mean ( u ) =1350
Standard Deviation ( sd )=700
Number ( n ) = 100
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)  

               
P(X > 1500) = (1500-1350)/700/ Sqrt ( 100 )
= 150/70= 2.1429
= P ( Z >2.1429) From Standard Normal Table
= 0.0161

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