The chance of an IRS audit for a tax return with over $25,000 in income is...

The chance of an IRS audit for a tax return with over $25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 8-year period. Assume each year is independent.

Give the distribution of X.

Expert Solution

The chance of an IRS audit for a tax return with over $25,000 in income, is about 2% per year.

We are interested in the random variable X, where X is the number of audits a person with income over $25,000 has, in a 8-year period.

Now, we note that the probability of having an audit in a randomly selected year, is 0.02.

Which means, the probability of not having an audit in a randomly selected year, is 1-0.02, ie. 0.98.

So, we have defined probabilities of success (having an audit, ie. 0.02) and failure (not having an audit, ie. 0.98), for each trial, which is a randomly selected year.

Given that the each year is independent.

And, the probabilities of success and failure together is 1.

So, all the conditions of binomial distribution are satisfied here.

So, we can conclude that

X , which is a random variable denoting the number of audits a person with income above $25,000 has in a 8-year period, follows Binomial distribution with parameters n = 8 and p = 0.02.

ie. X~Binomial(8,0.02).

orchestra answered 2 years ago

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The chance of an IRS audit for a tax return with over $25,000 in income is...

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