00:01
During a wisdom tooth removal procedure, one, two, three or four teeth are removed, depending on the patient.
00:07
The mean is 3 .14.
00:11
The standard deviation is 1 .24.
00:13
We take samples of size 7, and we want to look at the sample mean of these seven procedures.
00:21
What's the distribution of the sample mean? okay, so there are rules for adding up the means of different distributions.
00:29
I'm just going to state this rule.
00:32
The mean of x plus the mean of y is equal to the mean of x plus y.
00:38
So if you add up two distributions, you take the mean of that new distribution.
00:42
It's the sum of the means of the individual distributions.
00:45
They don't even have to be independent for this one.
00:48
Now, the same is not true of the standard deviation, but it is true of the variance.
00:54
Sigma squared x plus sigma squared y is sigma squared x.
00:59
They do need to be independent for that one.
01:02
Now if i rewrite this entirely in terms of x, so instead of adding up to different distributions, i'm going to add up seven independent observations of x.
01:13
So we'll get seven lots of mu x is equal to mu of the total, which i'll put as xt.
01:24
So that's the sum of seven observations of x.
01:28
The same for the variance.
01:36
Okay.
01:36
So for the mean, well, we're almost there...