00:01
We are told that the mean length of time a caller is placed on hold, so mu, is 180 seconds, with a standard deviation of 30 seconds.
00:11
We are not looking at individual calls, we are looking at a sample of size 1200.
00:17
And we want to look at a probability for the sample mean.
00:21
So how do we work with this? well, i'm going to refer to the central limit theorem, which states that as sample size increases, sample means become more and more normally distributed compared to the population.
00:34
If n is at least 30, you can treat them as approximately normally distributed.
00:39
So if you took every sample of this size, took the means plotted amount, you get something approximately normal.
00:47
The mean of the means is the same as the population mean.
00:51
The standard deviation of the sample means, or standard error, is sigma over root n.
00:56
So 30 over root 1200.
01:03
So i want to know the probability the sample mean is within 0 .1 seconds of the population mean...