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 5 cars will enter the car wash? Round your answer to four decimal places.

Answer 1

Answer: 0.1563

Explanation:

The Poisson distribution probability formula is given by :-

`P(X=x)=(e^(-\lambda)\lambda^x)/(x!)`, where
`\lambda` is the mean of the distribution and x is the number of success

Given : Cars enter a car wash at a mean rate of 2 cars per half an hour.

In an hour, the number of cars enters in car wash =
`\lambda=2*2=4`

Now, the probability that, in any hour, exactly 5 cars will enter the car wash is given by :-

`P(X=5)=(e^(-4)4^5)/(5!)=0.156293451851\approx0.1563`

Therefore, the required probability = 0.1563