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What is the probability you do not have to wait in line

**Assignment**

Customers call a help line to settle billing issues at a rate of 40 per hour. There are five representative responding to the calls on a first called first connected order. It takes about 5.6 minutes to settle the billing issue. Assume Poisson arrival and exponential service time for the representatives. However, 10% of the customers are not satisfied and are transferred to a supervisor after finishing with the representative. The supervisor takes exactly 10 minutes to settle the issue.

1) How many minutes does it take for customers from the moment they call until they are done if they are not connected to the supervisor?

2) How many minutes does it take for customers from the moment they call until they are done if they are also connected to the supervisor?

3) What is the probability you do not have to wait in line for the representative? Write it as a fraction such as 0.12 and not 12%.

4) What is the probability you do not have to wait in line for the supervisor if you are refereed to him/her? Write it as a fraction such as 0.12 and not 12%.

5) How many callers are either on hold or in the middle of service with a representative or the supervisor?

6) What is the minimum number of representative needed to be able to provide service?

7) What is the minimum number of representatives needed so that total time for callers who are not transferred to the supervisor will not exceed 6 minutes?

8) What is the minimum number of representatives needed so that total time for callers who are also transferred to the supervisor will not exceed 27 minutes?

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