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

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:

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

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