Answer to Question #156787 in Statistics and Probability for Daniel

Question #156787

1. The number of bank robberies that occur in Lagos is modeled to be Poisson distributed with mean of 1.8 per day. Find the probability of getting exactly three robberies in a day.

a. 0.3213

b. 0.1607

c. 0.8393

d. 0.4137



1
Expert's answer
2021-01-21T00:19:26-0500

In the poison distr ibution a discrete random variable XX has the following probability mass function,

P(X=x)=eλ.λxx!P(X=x)=\frac{e^{-\lambda }.\lambda ^x}{x!} , where λ\lambda is the mean of the distribution and x=0,1,2,3.....x=0,1,2,3.....\infty

Given that λ=1.8\lambda =1.8

Hence the required probability, P(X=3)=e1.8.(1.8)33!=0.1607P(X=3)=\frac{e^{-1.8 }.(1.8)^3}{3!}=0.1607

So probability of getting exactly three robberies in a day is =0.1607=0.1607


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