00:01
Patients arrive at a hospital emergency room at random with a rate of 6 per hour.
00:06
For part a of the question, we are asked to find the probability that during a 90 -minute period, the number of patients arriving is less than 2.
00:15
So let's say we define a random variable x as the number of patients arriving.
00:21
We want the probability that x is smaller than 2.
00:26
And this is for a duration of 90 minutes, which is 1 .5 hours.
00:32
Hours.
00:36
When we have some random phenomenon occurring, and we know the average rate of occurrence, in this case that's 6 arrivals per hour, then the number of arrivals in a given duration can be modeled as a poisson random variable.
00:52
So we can say x is a poisson random variable with an average rate of occurrence, denoted lambda, of 6 per hour.
01:03
The probability function for the poisson random variable is given by this formula, where the parameter mu, which is the mean of the distribution, is equal to the average rate of occurrence times the duration.
01:28
So 1 .5 hour duration means that mu is 6 times 1 .5, which is 9...