The number of cases of tetanus reported in the US in a single month has a Poisson distribution with a parameter of λ=4.0. What is the probability that five or more cases will be reported?

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Lindsey Gamble · Accepted Answer

Let X be the number of cases in 1 month  X follows Poisson distribution with parameter (rate) λ=4  X∼ Poisson (λ=4)  P(X≥5),λ=4  P(X≥5)=1−P(0≤X≤4) where P(0≤X≤4)=P(X=0)+P(X=1)  +P(X=2)+P(X=3)+P(X=4)  P(X=0)=e−λλ00!=e−4(4)00!=0.018316  P(X=1)=e−λλ11!=e−4(4)11!=0.073263  P(X=2)=e−λλ22!=e−4(4)22!=0.146525  P(X=3)=e−λλ33!=e−4(4)33!=0.195367  P(X=4)=e−λλ44!=e−4(4)44!=0.195367  Answer=1- (0.018316 + 0.073263 + 0.146525 + 0.195367 + 0.195367)=0.371163  Use excel function POISSON.DIST (X, mean, cumulative) to calculate  P(X≥5)=1−P(X≤4)=1−FX(4):  1-POISSON.DIST (4,4 TRUE)=0.37116306482  P(X≥5)=0.3712

The number of cases of tetanus reported in the US

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