Problem $7-23($Algo$)$

Customers enter the camera department of a store at an average rate of eight per hour. The department is staffed by one employee, who takes an average of $5\mathrm{.}0$ minutes to serve each arrival. Assume this is a simple Poisson arrival, exponentially distributed service time situation. $($Use the Excel spreadsheet Queue Models.$)$

a$-1.$ As a casual observer, how many people would you expect to see in the camera department $($excluding the clerk$)?$

Note: Round your answer to $2$ decimal places.

a$-2.$ How long would a customer expect to spend in the camera department $($total time$)?$

Note: Do not round intermediate calculations. Round your answer to $1$ decimal place.

b$.$ What is the utilization of the clerk?

Note: Do not round intermediate calculations. Round your answer to $1$ decimal place.

c$.$ What is the probability that there are more than two people in the camera department $($excluding the clerk$)?$

Note: Do not round intermediate calculations. Round your answer to $1$ decimal place.

d$.$ Another clerk has been hired for the camera department who also takes an average of $5\mathrm{.}0$ minutes to serve each arrival. How long would a customer expect to spend in the department now?

Note: Do not round intermediate calculations. Round your answer to $1$ decimal place.