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 there are exactly 3 customers in the system is
A)0.0000
B)0.1024
C)0.4096
D)0.5120

Question

Quizplus · Accepted Answer

The system is an M/M/1 queue. The probability of having exactly n customers in the system is given by (1-ρ)ρ^n, where ρ = λ/μ. Here, λ = 28 and μ = 35, so ρ = 28/35 = 0.8. The probability of having exactly 3 customers is (1-0.8) * 0.8^3 = 0.1024.

Consider an Espresso Stand with a Single Barista