The Internal Revenue Service is studying the category of charitable contribution

Question

The Internal Revenue Service is studying the category of charitable contributions. A sample of 20 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than $100,000. Of these 20 returns, 6 had charitable contributions of more than $1,000. Suppose 4 of these returns are selected for a comprehensive audit. You should use the hypergeometric distribution is appropriate. Because What is the probability exactly one of the four audited had a charitable deduction of more than $1,000? (Round your answer to 4 decimal places.) What is the probability at least one of the audited returns had a charitable contribution of more than $1,000? (Round your answer to 4 decimal places.)

Explanation / Answer

a. A hypergeometric distribution is used when we are sampling from a finite population without replacement.
    Therefore, the selected option is correct.

b. The hypergeometric distribution that can be used here has the following parameters:
    N = size of the population = 20
     k = no. of successes in the population (i.e. charitable contribution > $1000) = 6
     n = sample size = 4
     x = no. of successes in the sample

Therefore, probability that exactly 1 of the audited had a charitable deduction of more than $1000
     = P(x = 1)
     = kCx.N-kCn-x/NCn
     = 6C1.14C3/20C4
    = 0.45

c. Probability that at least 1 of the audited had a charitable contribution of more than $1000
    = 1 - Probability that none of the audited had a charitable contribution of more than $1000
    = 1 – P(x = 0)
    = 1 - kCx.N-kCn-x/NCn
    = 1 - 6C0.14C4/20C4
    = 1 – 0.21
    = 0.79

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.