Hacky Sack recently purchased and now manages a ski and snowboard rental shop near Silver Star Ski Resort. As part of his due diligence prior to the purchase, he established that he should expect to get 25 customers per hour. From his previous work experience, Hacky figures he can serve up to 30 customers per hour. As such, he figures that it does not make sense for him to have any customer waiting lines.

Prior to the grand re-opening of his newly acquired rental shop, he wants to be certain of his assumptions about potential queues in his shop. In exchange for unlimited rentals, a local OC student (that's you) agrees to examine the data and determine some characteristics of the potential queues. Assume Poisson arrivals and exponential service times.

1-What percent of time is Hacky busy serving customers?

2- Use your solution for Hacky Sack to answer this question. What is the average number of customers in the system?

3- Use your solution for Hacky Sack to answer this question. What is the average number of minutes a customer spends in the system?

4- Use your solution for Hacky Sack to answer this question. What is the average number of minutes a customer spends in the queue waiting for service?

5- Use your solution for Hacky Sack to answer this question. What is the average number of customers in the waiting line?