The number of cases of tetanus reported in the US in a single month has...

Deragz

Deragz

Answered

2022-01-18

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?

Answer & Explanation

Lindsey Gamble

Lindsey Gamble

Expert

2022-01-18Added 38 answers

Let X be the number of cases in 1 month
X follows Poisson distribution with parameter (rate) λ=4
X Poisson (λ=4)
P(X5),λ=4
P(X5)=1P(0X4) where P(0X4)=P(X=0)+P(X=1)
+P(X=2)+P(X=3)+P(X=4)
P(X=0)=eλλ00!=e4(4)00!=0.018316
P(X=1)=eλλ11!=e4(4)11!=0.073263
P(X=2)=eλλ22!=e4(4)22!=0.146525
P(X=3)=eλλ33!=e4(4)33!=0.195367
P(X=4)=eλλ44!=e4(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(X5)=1P(X4)=1FX(4):
1-POISSON.DIST (4,4 TRUE)=0.37116306482
P(X5)=0.3712

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