During off hours,cars arrive at a tollbooth on the East-West toll road at an average rate of 0.5 cars per minute.The arrivals are distributed according to the Poisson distribution.What is the probability that during the next minute,three cars will arrive?
A).0758
B).1255
C).0126
D).0613

Question

Quizplus · Accepted Answer

The given problem follows Poisson distribution with the following parameters:
λ = 0.5 (average rate of arrival per minute)

The probability of three cars arriving in the next minute can be calculated using the Poisson distribution formula:
P(X = 3) = (e^(-λ)* λ^X) / X!
P(X=3) = (e^(-0.5)* 0.5^3) / 3!
        = (0.08208499862) / 6
        = 0.0136808331
        ≈ 0.0126 (rounded to four decimal places)

Therefore, the probability that during the next minute, three cars will arrive is 0.0126 or 1.26% (approximately).
Hence, the best choice is (C).

During Off Hours,cars Arrive at a Tollbooth on the East-West