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Mathematics - Poisson Distribution - Compute Probability

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Patients arrive at the emergency room of Costa Valley Hospital at an average of 5 per day. The demand for emergency room treatment at Costa Valley follows a Poisson distribution.
(a) Compute the probability of exactly 0,1,2,3,4, and 5 arrivals per day.
(b) What is the sum of these probabilities, and why is the number less than 1?
Determine the probability of more than 3 visits for emergency room service on a given day.

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Solution Preview

m = 5; P(x) = (e^-m * m^x) / x!

(a) P(0) = (e^-5 * 5^0 / 0!) =0.0067

P(1) = (e^-5 * 5^1/ 1!) = 0.034

P(2) = (e^-5 * ...

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