Question

Cars enter a car wash at a mean rate of 2 cars per half an hour. What is the probability that, in any hour, exactly 2 cars will enter the car wash? Round your answer to four decimal places. Poisson Distribution

Answer 1

X1: # cars enter for wash a half hour duration. 
X2: # cars enter for wash the next half hour duration. 
X1 and X2 are independent Poisson variates (iid) with common mean 2. 

Then X=X1+X2 : # cars enter for wash in one hour duration is a Poisson variate with mean m = 2+2 
pmf is p(x) = e^-m m^x/ x! , x=0, 1, 2, ........ 

P[more than 3 cars] = 1 - P[3 or less cars] 
= 1 - [p(0)+p(1)+p(2)+p(3)]