Consider an espresso stand with a single barista.Customers arrive at 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 there are more than 2 customers in the system is
A)0.128
B)0.488
C)0.512
D)0.640

Question

Quizplus · Accepted Answer

First, we can find the utilization factor of the system:
Utilization Factor = Arrival Rate/Service Rate = 28/35 = 0.8

Next, we can use the formula for the probability of more than n customers in the system:
P(N > n) = (U/(1-U)) * ((U/(1-U))^n)

Using n=2, we get:
P(N > 2) = (0.8/(1-0.8)) * ((0.8/(1-0.8))^2) = 0.512

Therefore, the probability that there are more than 2 customers in the system is 0.512 or approximately 51.2%. So, the correct choice is C.

Consider an Espresso Stand with a Single Barista