Answer to Question #283679 in Statistics and Probability for Ahmed Hamza

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.