Find the probability of the following event.

Question

The number of accidents that occur at a busy intersection is Poisson distributed with a mean of 3.5 per week. Find the probability of the following event.

P(9 or more accidents occur in a week)=?

Answer 1

Let X denote the number of accidents in a week. Then X is Poisson with λ = 3.5, and we require P(X>9).

P(X>9) = 1 - P(X<8) = 1 - ∑P(X=k) for k=0 to k=8 = 1 - ∑ λ^k e^-λ / k! for k=0 to k=8 = 1 - 0.99013 = 0.00987

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