Consider an espresso stand with a single barista. Customers arrive to the stand at the rate of 28 per hour according to a Poisson distribution. Service times are exponentially distributed with a service rate of 35 customers per hour. The probability that the server is idle and a customer may be served is
A) 0.20.
B) 0.60.
C) 0.80.
D) 1.00.

Question

Quizplus · Accepted Answer

The probability that the server is idle is equal to the probability that the number of customers in the system is 0. This can be calculated using the formula P(0) = (1 - lambda/mu)^n, where lambda is the arrival rate, mu is the service rate, and n is the number of customers in the system. In this case, lambda = 28 per hour, mu = 35 per hour, and n = 0. Plugging these values into the formula, we get P(0) = (1 - 28/35)^0 = 1. Therefore, the probability that the server is idle is 1, or 100%.

Consider an Espresso Stand with a Single Barista