Q$1.$ Cuts$-$R$-$Us provides low$-$cost haircuts at a shopping center in Boise, Idaho. During the day, customers arrive at an average rate of $9$ per hour following an exponential distribution. After a customer is in a cosmetician$$s chair, it takes an average of $18$ minutes for the haircut to be completed, with the actual service time following a Poisson distribution.

a$.$ If there are $3$ cosmeticians on duty, how long will customers have to wait on average before receiving service and how many customers are typically waiting for service?

b$.$ If there are $4$ cosmeticians on duty, how long will customers have to wait on average before receiving service and how many customers are typically waiting for service?

c$.$ If there are $5$ cosmeticians on duty, how long will customers have to wait on average before receiving service and how many customers are typically waiting for service?

d$.$ If you managed this store, how many cosmeticians would you employ and why?

Solve it in Excel.