00:01
For this question, we are told that based on historical data, the average rate of arrivals of patients at a certain hospital is three every two hours.
00:11
And we're told to assume that patient arrivals are distributed according to a plus on distribution.
00:17
So that means that the number of patient arrivals in a given time duration follows a plus on distribution with a rate parameter of three per two hours.
00:32
The probability function for a quesan random variable is given by this formula.
00:38
This is the mean to the exponent x times e to the minus mean over x factorial for any non -negative integer.
00:50
Now here we want the probability that at least three but no more than eight patients arrive in a one hour period.
00:59
So our time period is one hour and the rate of arrival is three for two hours.
01:10
So that's 1 .5 per hour.
01:16
And so the mean for this poisson distribution is lambda times t or 1 .5.
01:26
So we want the probability that the number of patient arrivals is at least 3, but no more than 8.
01:35
This can be expressed as the probability that x is no bigger than 8, minus the probability that x is no bigger than 2.
01:44
And we can solve this using software such as excel...