Employees arrive at a cafeteria according to a Poisson process at an average rate of 30 employees per hour.The probability that after one employee arrives, the next one will arrive at least 3 minutes later is _________.
A)0.223
B)0.202
C)0.183
D)0.162
E)0.143

Question

Quizplus · Accepted Answer

The Poisson process implies that the time between arrivals follows an exponential distribution with parameter λ, where λ is the average rate of arrivals per unit time. Given λ = 30 employees per hour, or 0.5 employees per minute (since 30 employees/hour * 1 hour/60 minutes = 0.5 employees/minute), the probability that the time until the next arrival is at least t minutes is given by P(T ≥ t) = e^(-λt). For t = 3 minutes, P(T ≥ 3) = e^(-0.5*3) = e^(-1.5) ≈ 0.223.

Employees Arrive at a Cafeteria According to a Poisson Process