00:01
So we're looking at 25 pounds weights, and they follow a uniform distribution.
00:07
So i'm going to draw that.
00:08
We have x, the possible weights, the probability of that happening.
00:12
And the lowest weight is 24, the highest 26.
00:16
Anything in between these is equally likely.
00:19
So x follows a uniform distribution.
00:22
The parameters are the lower limit, the up limit.
00:26
We call these a and b.
00:27
The mean is a plus b over two.
00:32
This is symmetric.
00:34
The mean is also the median.
00:35
It's just the halfway point.
00:37
So the mean is 25.
00:39
The standard deviation is calculated by taking b minus a squared over 12, square rooting that.
00:48
So let's do that.
00:49
We have 26 minus 24.
00:50
So 2 squared is 4 over 12.
00:53
Square root that.
00:54
This is 1 over root 3.
00:58
So i'll just leave it in that.
00:59
Actually.
01:01
So that's part a, part b.
01:08
What about the distribution for the mean of a sample size of 100? so the central limit theorem tells me that as sample size increases, sample means become more and more normally distributed.
01:20
So with this, if i took every sample of size 100, took the means plotted amount, i would see something approximately normal.
01:27
The mean of the means is the same as the population.
01:33
The standard deviation of the sample of the means or standard error is sigma over root n.
01:39
So 1 over root 3 over root 100...