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The chance of an IRS audit for a return over $25,000 is about 2% per year. For 100 such taxpayers in one year, X ~ P(2). What is P(x=0), the probability that nobody in the sample is audited?
A0.3233
B0.1353
C0.8647
D2.0000
Answer & Solution
Correct answer: B. 0.1353
1. μ = np = (100)(0.02) = 2, so X ~ P(2).
2. Apply the Poisson pmf at x = 0: P(x=0) = (e^-2)(2^0)/0! = e^-2.
3. e^-2 ≈ 0.1353.
4. Option C is 1 - P(x=0), and option B is P(x≥3), a separate event.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.6 Poisson Distribution_
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