A telecommunication station is designed to receive a maximum

A telecommunication station is designed to receive a maximum of 12 calls per second. If the number of calls to the station is modeled as a Poisson random variable with a mean of 9 calls per second, what is the probability that the number of calls will exceed the maximum design constraint of the station? Round your answers to four decimal places (e.g. 98.7654).

Solution

If the station receives too many calls, then it receives x>12 number of calls were x is an number off into infinity. The only way for us to account for all of those possibilities is to find the chance of a x<=12 number of calls and subtract it from 1. This is kinda messy, but not too hard...

(e^(-9)*9^0)/0! + (e^(-9)*9^1)/1!+(e^(-9)*9^2)/2! +...+ (e^(-9)*9^12)/12! == 0.7059.

So 0.7059 is the chance of getting a call within the maximum design constraint. We subtract from 1:

1 - 0.7059 = 0.2941