Question

In the current tax year, suppose that 3% of the millions of individual tax returns have errors or are fraudulent. Although these errors are often well concealed, let’s suppose that a through IRS audit (done by you of course) will uncover them. If a random 100 tax returns are audited what is the probability that the IRS will uncover at most 4 fraudulent returns? Create an Excel spreadsheet that may give you an idea about this probability. Hint: Use the RAND() function for every tax return. The RAND() function generates a random number between 0 and 1. If the RAND() function gives you a number that is less than or equal to 0.03 then you can assume that the return contains error. Otherwise you can assume that the return does not contain any error. You can press F9 on your keyboard to regenerate a new instance. You may have to create enough instances to come up with a good approximation of the probability value. You can also find the exact probability using Binomial Distribution. What does it mean if an IRS auditor uncovers no more than 3 fraudulent/erroneous returns for every 100 tax returns?

Please in Excel.

Answer 1

If a random 100 tax returns are audited what is the probability that the IRS will uncover at most 4 fraudulent returns?

Using Binomial distribution

=BINOM.DIST(4,100,0.03,TRUE)

=0.8178