Solve the following problem. Use the provided Excel template for your calculations.

Probability of "n" Person in the System n Pn 0 0.2000 1 0.1600 2 0.1280 3 0.1024 4 0.0819 5 0.0655 6 0.0524 7 0.0419 8 0.0336 9 0.0268 10 0.0215

One physician on duty full-time works in a hospital emergency room. Previous experience has shown that emergency patients arrive according to a Poisson distribution with an average rate of 4 per hour. The physician can provide emergency treatment for approximately 6 patients per hour. The distribution of the physicians service time is a negative exponential. Determine each of the following:

a) Calculate the average probability of the system utilization b) What are the average numbers of patients in the waiting line (Lq) and in the system (L)? c) What are the average times that patients will spend in the waiting line (Wq) and in the system (W)? d) Calculate the probability of no patients in the system and the probability of 3 patients in the system.

Single Channel, Poisson Arrival, and Exponential Service Time (M/M/1) Single Channel, Poisson Arrival, and Exponential Service Time (M/M/1)