1. Variability, Chapter 8: Find a Doctor (EaD), 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. a) 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? b) How long in minutes) does a customer spend on average waiting on hold before they can start speaking to a representative from EaD? c) What is the average number of callers who are in Fan's call center system (either waiting or being served by the operator)? [Note: Average number of customers in the system does not need to be an integer because it is an average over time.] d) 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. [FYI, the cost of hiring a new qualified call center operator (identical to the current operators) is $20 per hour. Estimating the hourly call center cost allows you to decide if increasing the number of operators will reduce total staffing + line /penalty costs.] e) 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? f) Calculate the value of cd?, the SCV (squared coefficient of variation) of the inter-departure times from the system g) Suppose the call center operator always works through a computer technology interface, which has recently been prone to random, preemptive breakdown due, among other things, to hacker activity. [When the technology is down, the operator also cannot work.] The computer technology resource is subject to random failure with mean time to failure (MTTF or uptime), mg= 8 hours, and mean time to repair (MTTR or downtime), Mr = 20 minutes. Repair time is exponentially distributed with SCV, C7 = 1.5. Calculate the mean and SCV of the effective call processing time, te and ce?, after incorporating computer technology breakdown