00:01
In this question, we are told that patients arrive at a hospital emergency at a rate of 6 per hour.
00:09
And for question 1, we are asked for the probability of two arrivals during the next 30 minutes.
00:17
So let's assume that the arrivals follow a poisson distribution.
00:32
When we are given some rate, some average rate of arrivals over some time period and no other information, the poisson distribution is usually the appropriate model.
00:45
And the probability mass function for the poisson random variable is given by this formula.
01:14
So for one we want the probability of two arrivals in half an hour.
01:30
Now here we have lambda is equal to 6 and t is half an hour.
01:39
It's 30 minutes.
01:40
We want to make sure that we keep our units consistent.
01:44
So we're going to state it in terms of number per hour.
01:48
So our basic time unit is the hour.
01:57
So this is equal to 6 times .5 to the exponent 2 times e to the minus 6 times .5 divided by 2 factorial.
02:18
And this comes out to .2240.
02:27
Then for question 2 we are asked for the probability of 3 arrivals during the next 60 minutes...