The emergency room at Hospital Systems, Inc (HIS) serves patients who arrive according to a Poisson...
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?
Homework Answers
=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
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