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$\text{'}$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 $3$ cosmetician$\text{'}$s 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 $4$ cosmetician$\text{'}$s 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 $5$ cosmetician$\text{'}$s 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

cosmetician$\text{'}$s would you employ and why?