Moore, Aiken, and Payne is a dental clinic serving the needs of the general public on a first-come, first-served basis. The clinic has three dental chairs, each staffed by a dentist. Patients arrive at the rate of five per hour, according to a Poisson distribution, and do not balk or renege. The average time required for a dental checkup is 30 minutes, according to an exponential distribution.

a. What is the probability that no patients are in the clinic?

b. What is the probability that six or more patients are in the clinic?

c. What is the average number of patients waiting in the lobby?

d. What is the average total lime that a patient spends in the clinic?