00:01
A population has a mean, mu, of 494, a standard deviation, sigma, of 20.
00:08
We're taking many samples of size 48.
00:11
We want to know the mean and standard deviation for all of these sample means.
00:16
So i don't know the shape of the original distribution, but i do know that if i take every possible sample of size 48, take the sample means and plot them out, i will get something approximately normal.
00:33
This is because of the central limit theorem, which states that as sample size increases, sample means become more and more normally distributed compared to the population.
00:44
If n is at least 30, you can treat them as approximately normal.
00:48
So the answer to part c is approximately normal.
00:53
For parts a and b, the central limit theorem does detail these.
00:57
I will write them down and then prove them afterwards.
01:01
Mean of the means is just the same as the population mean.
01:05
Standard deviation of the sample means, or standard error, is sigma over root n...