Question

At a walk-in clinic, assume that on average exactly 6.00 patients arrive per hour, that this is true regardless of the day and the hour of the day, and that it is independent of how many patients have already arrived that hour.

e) It is now 10:00 AM. A patient arrived 9:45 AM (15 minutes ago), and no other patient has arrived since then. What is the probability that the next patient will arrive before 10:30 AM?

Answer 1

Ans:

Given that

lambda=6 per hour

e)Use exponential distribution with lambda=6 per hour

Exponential distribution is memoryless,so it does not matter if some patient arrived or not before 10 am.We will consider time interval from 10 AM to 10:30 AM i.e. 30 minute time interval.

lambda=6 per hour =0.1 per minute

(6/60=0.1 per minute)

P(T<30 min)=1-exp(-0.1*30)=0.9502