If arrivals occur at a mean rate of 3.6 events per hour,the exponential probability of waiting more than 0.5 hour for the next arrival is
A)0.2407
B)0.1653
C)0.1222
D)0.5000

Question

Quizplus · Accepted Answer

We can model the time between arrivals as an exponential distribution with a rate parameter of λ = 3.6 (since the mean and the rate are equal for an exponential distribution). Then, the probability of waiting more than 0.5 hour for the next arrival is:
P(X > 0.5) = e^(-λx) = e^(-3.6*0.5) = 0.1653
So, the answer is B.

If Arrivals Occur at a Mean Rate of 3