Question

A life insurance salesman sells on the average 3 life insurance policies per week. Use poisson's law to caculate the probability that in a given week he will sell 2 or more policies but less than 5 policies.

Answer 1

The probability of selling 2 or more, but less than 5 policies is

$P(2\le X<5)$

$=P\left(x_2\right)+P\left(x_3\right)+P\left(x_4\right)$

$=\frac{e^{-3}{3}^2}{2!}+\frac{e^{-3}{3}^3}{3!}+\frac{e^{-3}{3}^4}{4!}$

$=0.61611$