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

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) ]