# he Atlas Health Club has one tanning booth for its customers. Users of the tanning booth spend exactly 5 minutes in the facility. Customers arrive at the booth according to a Poisson process at a mean rate of 8 per hour. A. What is the average time a customer must wait in line to use the tanning booth? B. What is the average number of customers waiting to use the tanning booth? C. What is the probability that there will be no users in the whole system? D. If the time a user of the tanning booth spends in the facility is 5 minutes on average and the time is exponentially distributed: (d1) How would your answer in sub questions (a) and (b) change? (d2) What is the probability that there will be no users in the whole system?

he Atlas Health Club has one tanning booth for its customers. Users of the tanning booth spend exactly 5 minutes in the facility. Customers arrive at the booth according to a Poisson process at a mean rate of 8 per hour.

A. What is the average time a customer must wait in line to use the tanning booth?

B. What is the average number of customers waiting to use the tanning booth?

C. What is the probability that there will be no users in the whole system?

D. If the time a user of the tanning booth spends in the facility is 5 minutes on average and the time is exponentially distributed:

(d1) How would your answer in sub questions (a) and (b) change?

(d2) What is the probability that there will be no users in the whole system?