 Probability Questions

Subject Mathematics General Statistics

Question

1. Zac Richardson, CPA, has a stack of 22 tax returns to complete before the April 15th deadline. Of the 22 tax returns, 13 are from individuals, 7 are from businesses, and 2 are from charitable organizations. He randomly selects two returns.
a. What is the probability that both are businesses?
b. What is the probability that at least one is a business?

2. Ella exercises regularly. Her fitness log for the last 12 months shows that she jogged 25% of the days, rode her bike 18% of the days, and did both on 12% of the days. What is the probability that Ella would do at least one of these two types of exercises on any given day?

3. Carlos works in a tax office with 5 other CPAs. There are six parking spots beside the office. If they all drive to work, how many different ways can the cars belonging to the CPAs be arranged in the six spots?

4. IRS data show that 16% of personal tax returns reporting an adjusted gross income more than \$1,000,000 will be subject to a computer audit. This year a CPA completed 18 returns with adjusted gross incomes more than \$1,000,000. The CPA wants to know the likelihoods that the returns will be audited.
a. What probability distribution applies to this situation?
b. What is the probability exactly one of these returns is audited?
c. What is the probability at least one of these returns is audited?

5. For certain personal tax returns, the IRS will compute the amount to refund a taxpayer. Suppose the Harrisburg office of the IRS processes an average of 4 returns per hour that require a refund calculation.
a. What probability distribution applies to this situation?
b. What is the probability the IRS processes exactly four returns in a particular hour that require a refund calculation?
c. What is the probability the IRS does not compute a refund on any return in an hour?
d. What is the probability the IRS processes at least one return in a particular hour that requires a refund calculation?

6. A CPA studies the number of exemptions claimed on tax returns. The data are summarized in the following table.
Exemptions Percent
1                    20
2                    50
3                    20
4                    10
a. What is the mean number of exemptions claimed?
b. What is the variance of the number of exemptions claimed?

7. The IRS reports that the mean refund for a particular group of taxpayers was \$1,600. The distribution of tax refunds follows a normal distribution with a standard deviation of \$850.
a. What percentage of the refunds are between \$1,600 and \$2,000?
b. What percentage of the refunds are between \$900 and \$2,000?
c. What percentage of the refunds are between \$1,800 and \$2,000?
d. 95% of the refunds are for less than what amount?

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