Top Cutz International Barbershop is a popular haircutting and styling salon near the campus of the KCA University, Ruaraka. Four barbers work full$-$time and spend an average of $15$ minutes on each customer. Customers arrive all day long at an average rate of $12$ per hour. When they enter, they take a number to wait for the first available barber. Arrivals tend to follow the Poisson distribution, and service times are exponentially distributed.REQUIRED$($a$)$ What is the probability that the shop is empty? $[1$Mark$]($b$)$ What is the average number of customers in the barbershop? $[2$Marks$]($c$)$ What is the average time spent in the shop? $[2$Marks$]($d$)$ What is the average time that a customer spends waiting to be called to the barber chair? $[2$Marks$]($e$)$ What is the average number waiting to be served? $[1$Mark$]($f$)$ What is the shop's utilization factor? $[1$Mark$]($g$)$ Sal's is thinking of adding a fifth barber. How will this affect the utilization rate? $[1$Mark$]$