Problem $10-16($Algo$)$

Customers enter the camera department of a store at the average rate of six 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 Exhibit $10\mathrm{.}9.$

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.

Number of people

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

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

Average total time

minutes

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

Note: 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: Round your intermediate calculations to $3$ decimal places and final answer to $1$ decimal place.

Probability

d$.$ Another clerk has been hired for the camera department who also takes an average of $5$ minutes to serve each arrival. How long

would a customer expect to spend in the department now?

Note: Round your answer to $1$ decimal place. Use the closest value of $\frac{}{}$ in Exhibit $10\mathrm{.}9$ when determining $L_q($i$.$e$.,$ do not

interpolate$).$