A tax auditor is selecting a sample of 66 tax returns for an audit. If 22 or mor
ID: 2931913 • Letter: A
Question
A tax auditor is selecting a sample of 66 tax returns for an audit. If 22 or more of these returns are "improper," the entire population of 5050 tax returns will be audited. Complete parts (a) through (e) below.
a. What is the probability that the entire population will be audited if the true number of improper returns in the population is15?
(Round to four decimal places as needed.)
b. What is the probability that the entire population will be audited if the true number of improper returns in the population is 20?
(Round to four decimal places as needed.)
c. What is the probability that the entire population will be audited if the true number of improper returns in the population is 55
(Round to four decimal places as needed.)
d. What is the probability that the entire population will be audited if the true number of improper returns in the population is 10?
(Round to four decimal places as needed.)
e. Discuss the differences in the results, depending on the true number of improper returns in the population. Choose the correct answer below.
A.
The probability that the entire group will be audited is not very sensitive to the true number of improper returns in the population. The probability increases as the true number increases, but only slightly.
B.
The probability that the entire group will be audited is very sensitive to the true number of improper returns in the population. If the true number is very low, the probability is very low. If the true number is very high, the probability is very high.
C.
The probability that the entire group will be audited is not very sensitive to the true number of improper returns in the population. The probability decreases as the true number increases, but only slightly.
D.
The probability that the entire group will be audited is very sensitive to the true number of improper returns in the population. If the true number is very low, the probability is very low. If the true number is very high, the probability is very low.
Explanation / Answer
a.
If the true number of improper returns in the population is 15, we cannot get more than 15 improper returns in a sample of 66 tax returns. So the the probability that the entire population will be audited will be 0.
b.
This is similar to part (a). If the true number of improper returns in the population is 20, we cannot get more than 20 improper returns in a sample of 66 tax returns. So the the probability that the entire population will be audited will be 0.
c.
The true number of improper returns in the population is 55. So, the probability of selecting an improper return = 55/5050 = 0.0109
Using binomial distribution calculator, the probability to get more than 22 or more of these returns out of 66 returns, with the probability of improper return as 0.0109 is near 0.
So, the probability that the entire population will be audited if the true number of improper returns in the population is 55 is 0.
d.
This is similar to part (a). If the true number of improper returns in the population is 10, we cannot get more than 10 improper returns in a sample of 66 tax returns. So the the probability that the entire population will be audited will be 0.
e.
Let us suppose the true number of improper returns in the population is very high and close to 2000.
So, the probability of selecting an improper return = 2000/5050 = 0.396
Using binomial distribution calculator, the probability to get more than 22 or more of these returns out of 66 returns, with the probability of improper return as 0.396 is near 0.82
So, the probability that the entire population will be audited if the true number of improper returns in the population is 2000 is 0.82
Thus, the the probability that the entire population will be audited increases if the true number of improper returns increases. So, B is the correct option.
B.
The probability that the entire group will be audited is very sensitive to the true number of improper returns in the population. If the true number is very low, the probability is very low. If the true number is very high, the probability is very high.
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