Customers arrive at Rich Dunn$$s Styling Shop at a rate of $3$ per hour, distributed in a Poisson fashion.

Rich$$s service times follow a negative exponential distribution, and Rich can complete an average of $5$ haircuts per hour.

a$)$ Find the average number of customers waiting for haircuts.

b$)$ Find the average number of customers in the shop.

c$)$ Find the averge time a customer waits until it is his or her turn.

d$)$ Find the average time

a customer spends in the shop.

e$)$ Find the percentage of time that Rich is busy.