Twelve customers arrive at the lunch counter at George's Happy Hog per hour and select the hickory smoked meat du jour along with a side and soda for $5. The server doubles as the cashier and can take and fill an order in three minutes on average. What is the likelihood that there are two customers in the system at the George's Happy Hog if the times can be assumed as exponentially distributed?
A) .33
B) .25
C) .144
D) .05

Question

Quizplus · Accepted Answer

We can model the arrival rate as λ=12 customers/hour, and the service rate as μ=20 customers/hour (since it takes an average of 3 minutes to serve one customer).

To find the probability of two customers in the system, we can use the formula for the steady-state probability of n customers in the system:

P(n) = (1 - ρ)ρ^n

where ρ = λ/μ is the traffic intensity.

Plugging in our values, we get:

ρ = λ/μ = 12/20 = 0.6

P(2) = (1 - 0.6)*(0.6)^2 = 0.144

So the likelihood that there are two customers in the system is 0.144, or 14.4%.

Therefore, the correct answer is C.

Twelve Customers Arrive at the Lunch Counter at George's Happy