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The average number of children a Spanish woman has in her lifetime is 1.47, so X ~ P(1.47). What is P(x=0), the probability a randomly chosen Spanish woman has no children?
A0.2299
B0.5679
C0.4321
D1.4700
Answer & Solution
Correct answer: A. 0.2299
1. Apply the Poisson pmf at x = 0: P(x=0) = e^-μ = e^-1.47.
2. e^-1.47 ≈ 0.2299.
3. So about 23% of Spanish women are expected to have no children under this model.
4. Option B is P(x≤1), and option C is P(x≥2), both different events from P(x=0).
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.6 Poisson Distribution_
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