The chance of an IRS audit for a tax return with over \($25,000\) in income is about 2% per year. Suppose that 100 people with tax returns over \($25,000\) are randomly picked. We are interested in the number of people audited in one year. Use a Poisson distribution to anwer the following questions.

a. In words, define the random variable X.

b. List the values that X may take on.

c. How many are expected to be audited?

d. Find the probability that no one was audited.

e. Find the probability that at least three were audited.