A bus company has a fleet of $20$ buses and a maintenance facility. At midnight, the buses arrive at

the maintenance facility with exponential inter$-$arrival times. The mean inter$-$arrival time is $10$

minutes. The facility consists of one inspection station and one repair station. Both stations serve

the buses on a first$-$come$-$first$-$serve basis. When a bus arrives, it is first moved to the inspection

station for inspection. Historical data shows that $30\%$ of the buses need repairs. Buses that do

not need to be repaired leave the facility right away. Buses that need repair are moved to the

repair station immediately after inspection. The inspection times have a continuous uniform

distribution from $5$ to $10$ minutes. The repair times have a gamma distribution with a mean and

standard deviation of $20$ and $15$ minutes respectively.

Use Microsoft Excel to simulate the maintenance operation with $30$ replications. Estimate the

time to complete the maintenance for all buses, utilization for both stations and the average stay

time of the buses in the facility with $99\%$ confidence intervals. Save the Excel file as a Macroenabled worksheet with the filename $$Q$2.$xlsm$.$