00:01
So for this problem, to begin, i'll note that the real trick for this is figuring out what the appropriate approach is.
00:10
We know that the mean value for a random variable is equal to 1 .5, and the variance for a random variable is equal to 1.
00:21
And we are trying to find the probability that 100 customers can be served in less than 2 hours.
00:26
So one way of thinking about that would be that if we have that, let's call xi as being the time for the ith customer, time for the ith customer, we could think of this as we're looking for the probability that the sum from i equals 1 up to 100 of xi is less than or equal to two hours, which would be 120 minutes.
01:02
But one thing that we should note is that if we consider what a sample mean is, well, we know that the sample mean would be equal to the sum from, in this case, i equals 1 up to 100, of xi, divided by the sample size, which would be 100.
01:24
So we can then note that if the sum, if we're trying to see whether or not the sum of all of our xi values is less than or equal to 120, that would be equivalent to, asking for the probability that the sample mean value is less than or equal to 120 over 100, which would be 1 .2.
01:45
So, really, this is a probability problem with sample mean values.
01:51
Now, i'll note the next step here, we do not know the distribution of the xi values.
02:05
But that doesn't actually matter...