Final answer:
The average server utilization of the system is 83.33%, calculated by dividing the arrival rate (10 customers per hour) by the service rate (12 customers per hour).
Step-by-step explanation:
To calculate the average server utilization in the system with an average service rate of twelve customers per hour and an arrival rate of ten customers per hour, we apply the formula for server utilization, which is the ratio of the arrival rate (\(\lambda\)) to the service rate (\(\mu\)).
Server Utilization = \(\frac{\lambda}{\mu}\) = \(\frac{10}{12}\) = 0.8333 or 83.33%.
This means that the server is busy 83.33% of the time providing service to customers, and there is a 16.67% idle time.