Find a Doctor (FaD), is a small startup that helps people find a physician that best meets their needs (location, insurance accepted, etc.). During a relatively slow time for them, they have 5 staff members in a call center taking calls from customers. On average, one call arrives every 6 minutes with a standard deviation of 6 minutes. Each staff member spends 18 minutes with each customer on average, with a standard deviation of 27 minutes.

1)What is the probability that one of their staff members is busy (as a %), i.e., what percentage of time are the staff members busy, on average?

2)How long (in minutes) does a customer spend on average waiting on hold before they can start speaking to a representative from FaD?

3)What is the average number of callers who are in FaD's call center system (either waiting or being served by the operator)?

4)Suppose that for every minute of time a caller waits on hold for service it costs the call center 75 cents in phone line charges and service contract penalty. Estimate the hourly call center cost for caller wait times.

5)If you were asked to list general mechanisms to improve a call center such as FaD, what two things would you target for improvement and how might the improvement be achieved?

6)Calculate the value of cd2, the SCV (squared coefficient of variation) of the inter-departure times from the system.