$2.$ You are the director of the customer service center in Company Alpha. You find that the mean

time between calls to the center is $6$ minutes with standard deviation of $4$ minutes. The effective

response time is $11$ minutes with a standard deviation of $20$ minutes.

$($a$)$ Identify the following parameters:

ta: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\backslash$sigma a: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ ca$2$: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ ra: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

te: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\backslash$sigma e: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ ce$2$: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ re: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$($b$)$ Suppose the customer call center has $3$ servers who answer calls. Find the following metrics:

u: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ cd$2$: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$($c$)$ Assume that $100\%$ of answered calls are then recorded and immediately monitored for the

quality purposes. What is the arrival variability at the Quality Office? Why?

ca$2$: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$