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.
Accepted Solution
A:
Answer: 0.1563Step-by-step explanation:The Poisson distribution probability formula is given by :-[tex]P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}[/tex], where [tex]\lambda[/tex] 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 = [tex]\lambda=2\times2=4[/tex]Now, the probability that, in any hour, exactly 5 cars will enter the car wash is given by :-[tex]P(X=5)=\dfrac{e^{-4}4^5}{5!}=0.156293451851\approx0.1563[/tex]Therefore, the required probability = 0.1563