If cars arrive to a service center randomly and independently at a rate of 5 per hour on average, what is the probability that exactly 5 cars will arrive during a given hour?
A) 0.1755
B) 0.6160
C) 0.1277
D) Essentially zero

Question

Quizplus · Accepted Answer

The number of cars arriving follows a Poisson distribution with a mean (λ) of 5. The probability of exactly k events (k=5) in a Poisson distribution is given by P(X=k) = (e^(-λ) * λ^k) / k!. Plugging in the values, P(X=5) = (e^(-5) * 5^5) / 5! = 0.1755.

If Cars Arrive to a Service Center Randomly and Independently