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A rule of thumb governs when the Poisson distribution can approximate a binomial distribution. According to that rule, what must be true of n and p?
An is at most 20 and p is at least 0.05
Bn equals p exactly, regardless of size
Cn is at least 20 and p is at most 0.05
Dn and p must both exceed one
Answer & Solution
Correct answer: C. n is at least 20 and p is at most 0.05
1. A glossary entry states the approximation rule explicitly.
2. It requires n to be large, specifically at least 20, and p to be small, specifically at most 0.05.
3. Under those conditions the Poisson distribution gives probabilities close to the true binomial values.
4. Options A, B, and D each invert or invent a condition that is never actually stated.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.3 Binomial Distribution_
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