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, no more than 4 cars will enter the car wash

Answer 1

1.56499409

Explanation:

We solve using Poisson Distribution

P = λ^k × e^-λ/k!

λ is the average of events = mean rate of 2 cars per half an hour = 2 × 2 = 4

e is the euler's number

k is the number of events you want to know the probability = no more than 4

= ≤ 4

Hence:

P(≤ 4) = 4^4 × e^-4/4! + 4^3 × e^-4/3! + 4^2 × e^-4/2! + 4^1× e^-4/1! + 4^0× e^-4/0!

P(≤ 4) = 0.1953668148 + 0.1953668148 + 1.0826822659 + 0.0732625556 + 0.0183156389.

P(≤ 4) = 1.56499409