Question

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

Answer 1

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

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

Given that $\lambda =1.8$

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

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