Patients arrive at a 1-doctor clinic according to a Poisson distribution at the rate of 20 patients

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Patients arrive at a 1-doctor clinic according to a Poisson distribution at the rate of 20 patients per hour. The waiting room does not accommodate more than 14 patients.

Examination time per patient is exponential, with a mean of 8 minutes.

(a) What is the probability that an arriving patient will not wait?

(b) What is the probability that an arriving patient will find a seat in the room?

(c) What is the expected total time a patient spends in the clinic?

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