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 takes 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 exponential distribution with a rate of 3 per minute has a mean of 1/3 minute. The probability that the time between arrivals is less than 1/2 minute is given by the cumulative distribution function: 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