Drivers arrive at a toll booth at a rate of 3 per minute during peak traffic periods.The time between consecutive driver arrivals follows an exponential distribution.What is the probability that it will take less than 1/2 of a minute between consecutive drivers?
A)0.167
B)0.223
C)0.777
D)0.5
E)1

Question

Quizplus · Accepted Answer

The rate (λ) is 3 drivers per minute, so the mean time between arrivals is 1/3 minute. The exponential distribution gives P(X < x) = 1 - e^(-λx). For x = 0.5, P(X < 0.5) = 1 - e^(-3*0.5) = 1 - e^(-1.5) ≈ 0.777.

Drivers Arrive at a Toll Booth at a Rate of 3