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 a 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

Using the Poisson distribution formula: 
P(X=k) = (e^(-λ) * λ^k) / k!
Where:
λ = average rate of arrivals = 0.5 cars per min
k = number of arrivals we want to find = 3

P(X=3)= (e^(-0.5)*(0.5^3))/3!
= 0.0126

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

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