A grocery store in a small town has a single check-out counter to service its customers. Customers wait in a single line at the checkout counter and are served on a first-come, first-served basis. On average, 25 customers per hour arrive at the checkout counter and customer arrivals are assumed to have a Poisson distribution. The employee at the checkout counter can serve the customers at an average rate of 30 customer per hour, with the service time being described by a negative exponential distribution.

Determine:

1. Capacity utilization for the system

2. Average number customers waiting in line (queue)

3. Average time a customer spends in the system (waiting time plus service time)

4. Probability that five customers are in the system