Statistics IRS Audits The Hemingway Financial Company prepares tax returns for i

Question

Statistics

IRS Audits The Hemingway Financial Company prepares tax returns for individuals. (Motto: "We also write great fiction.") According to the internal Revenue Service. Individuals making $25,000-$50,000 are audited at a rate of 1%. The Hemingway Company prepares five tax returens for individuals in that tax bracket, and three of them are audited. Find the probability that when 5 people making $25.000-$50,000 are randomly selected, exactly 3 of them are audited. Find the probability that at least 3 people are audited. Based on the preceding result, what can you conclude about the Hemingway customer? Are they just unlucky, or are they being targeted for audits?

Explanation / Answer

Total number of cases depending on the number of audits done out of 5= 5C0 + 5C1 + 5C2 + 5C3 + 5C4 + 5C5 = 32

i) when 3 out of 5 randomly selected people are audited
prob. = (5C3)/(5C0 + 5C1 + 5C2 + 5C3 + 5C4 + 5C5) = 10/32 = 0.3125

ii) P(at least 3 people are audited)= 1- P(2 people audited) - P(1 people audited) - P(no one audited)
= 1 - (5C2)/32 - (5C1)/32 - (5C0)/32 = 0.5

iii) The prob. will be same for any other firm also. Hence, the Hemingway is just unlucky.

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