Question

The emergency room at Hospital Systems, Inc (HIS) serves patients who arrive according to

a Poisson distribution at the rate of 9 per hour. Treatment takes an average of 6 minutes and

the treatment times can be considered to follow an exponential distribution. What is the

(a) minimum number of doctors required so that at least 70% of the arriving patients can

receive treatment immediately?

(b) minimum number of doctors required so that the average time a patient waits for

treatment is no more than 30 minutes as advertised? No more than 15 minutes?

Answer 1

=9 per hour

=1/6 patients per minute = 0.167 per min = 10 patients per hour

Answer a= Let us assume that one patient is treated by one doctor.

So the probability of the arriving patient to wait= 9/10 =0.9=90%

Probability of the incoming patient to be servied= 7/10 = 70%

So the number of doctors required=7