If arrivals occur at a mean rate of 3.6 events per hour, the exponential probability of waiting less than 0.5 hour for the next arrival is:
A).7122.
B).8105.
C).8347.
D).7809.

Question

Quizplus · Accepted Answer

The parameter λ of the exponential distribution can be calculated as the reciprocal of the mean rate, so λ = 1/3.6 = 0.2778.
The probability of waiting less than 0.5 hour for the next arrival can be calculated as:
P(X < 0.5) = 1 - e^(-λt) = 1 - e^(-0.2778*0.5) ≈ 0.8347
Therefore, the best choice is C.

If Arrivals Occur at a Mean Rate of 3