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

Question

Quizplus · Accepted Answer

The exponential distribution is given by the formula $P(X < x) = 1 - e^{-\lambda x}$, where $\lambda$ is the rate of occurrence (3 per minute in this case) and $x$ is the time interval (1/2 minute). Substituting these values, we get $P(X < 1/2) = 1 - e^{-3 \times 1/2} = 1 - e^{-1.5} \approx 0.777$.

Drivers Arrive at a Toll Booth at a Rate of 3