Cars cross a bridge at a uniform rate and the number of cars

Cars cross a bridge at a uniform rate and the number of cars in non-overlapping time intervals are independent. On average 12 cars pass the bridge each minute. Find the probability that 17 or more cars pass the bridge in a one minute time interval.

(Please note that this is not a Poisson distribution).

Solution

Given X follows Poisson distribution with mean=12 per minute

P(X=x)=(12^x)*exp(-12)/x! for x=0,1,2,...

So the probability is

P(X>=17) =1-P(X=0)-P(X=1)-...-P(X=16)

=1-(12^0)*exp(-12)/1-...-(12^16)*exp(-12)/16!

=0.101291