Question

Suppose the average number of calls received by an operator in one minute is 2. What is the probability of receiving 10 calls in 5 minutes? 

Answer 1

Let $X$ be a random variable representing the number of calls received. Then $X$ follows a Poisson distribution given as,

$p(X=x)={e^{-\lambda}\lambda^x\over x!}, \space x=0,1,2,3,4,....$

with a rate of 2 calls per minute.

For 5 minutes, the value of the parameter $\lambda=5\times2=10$

The probability of receiving 10 calls is,

$p(X=10)={e^{-10}10^{10}\over10!}= 0.12511$

Therefore, the probability of receiving 10 calls in 5 minutes is 0.12511.