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Mrs. Plum's cats wake her up an average of ten times per week, so X ~ P(10). What is P(x≤5), the probability her cats wake her up no more than five times next week?
A0.5000
B0.0671
C0.9329
D0.0378
Answer & Solution
Correct answer: B. 0.0671
1. With μ = 10, X ~ P(10) models the weekly wake-up count.
2. P(x≤5) sums the Poisson pmf for x = 0 through x = 5 with μ = 10.
3. That cumulative sum evaluates to about 0.0671.
4. Option C is the complement, P(x>5), not the value asked for, so it does not answer the question.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.6 Poisson Distribution_
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