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:
[tex]\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}[/tex]Probability that exactly 5 cars will enter the car wash in an hour = 0.1606
