In a recent year the U.S. Internal Revenue Service (IRS) received 132,275,830 individual tax returns. The actual Rower 0; each type of individual return received by the IRS during, the year is given below:
|
Type of Return
|
Total Returns Filed
|
|
1040A. Income Under $25,000
|
31,675,935
|
|
Non 1040A, income Under $25,000
|
20,295,694
|
|
Income $25,000-$50,000
|
30,828,932
|
|
Income $50,000-$100,000
|
26,463,973
|
|
Income $100,000 & Over
|
12,893,802
|
|
Schedule C. Receipts Under $25,000
|
3,376,943
|
|
Schedule C, Receipts $25,000-$100,000
|
3,867,743
|
|
Schedule C, Receipts $100,000 & Over
|
2,288,550
|
|
Schedule F. Receipts Under $100,000
|
318,646
|
|
Schedule F, Receipts $100,000 & Over
|
265,612
|
Suppose an IRS auditor must randomly select and examine an individual return.
a. What is the probability that the auditor will select an individual return from the 1040A, Income Under $25,000 category?
b. What is the probability that the selected return did not use Schedule C?
c. What is the probability that the selected return reported income or reciepts of $100,000 & over?
d. In 2006 the IRS examined 1% of all individual returns. Assuming the examined returns were evenly distributed across the ten categories in the above table, how many returns from the Non I040A, Income $50,000-$100,000 category were examined.
e. When examining 2006 individual income tax returns, IRS auditors found that individual taxpayers still owed $13,045,221,000 in income taxes due to errors the individual taxpayers had made on this year's individual income tax returns (this is referred to by the IRS as recommended individual taxes). Use this information to estimate the recommended additional taxes for the Schedule C, Receipts $100,000 & over category.