Question

Cars enter a car wash at a mean rate of 3 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:

Probability that exactly 5 cars will enter the car wash in an hour = 0.1606

Step-by-step explanation:

The mean rate = 3 cars per half an hour

The mean rate in 1 hour, λ = 3(2) = 6

Probability that exactly 5 cars will enter the car wash in an hour, P(X = 5)

Using the Poisson distribution formula:

`\begin{gathered} P(X=x)=(e^(-\lambda)\lambda^x)/(x!) \\ \\ P(X=5)=(e^(-6)(6^5))/(5!) \\ \\ P(X=5)=(19.2748)/(120) \\ \\ P(X=5)=0.1606 \end{gathered}`

Probability that exactly 5 cars will enter the car wash in an hour = 0.1606