00:01
Of cables has a mean of 2 ,000 pounds and the standard deviation of 100 pounds and is normally distributed.
00:13
Now we're going to take a sample of 20 cables.
00:26
So the sample size is 20.
00:30
Then we want to look at the distribution of the sample means.
00:37
Okay, so this data over here is for the distribution of all the cables, okay? the mean of all the cables is 2 ,000 pounds.
00:54
The standard deviation is 100 pounds, and the distribution of all the cables is normally distributed.
01:02
But we're taking a sample of 20 cables.
01:04
The distribution of sample means will also be approximately normally distributed.
01:13
It will have the same mean as the distribution, the normal distribution 2000.
01:22
But the standard deviation of the sample means called the standard error is given by the standard deviation of the entire distribution divided by the square root event.
01:37
So standard deviation for the distribution of all the cables was 100.
01:45
We're taking a sample of 20.
01:48
So our standard error, or the standard deviation for the distribution of our sample means, where the sample size are 20 cables, standard error will be the standard deviation of the distribution of all cables divided by the square root of your sample.
02:07
Size, the square root of 20.
02:16
Okay, for our normal distribution of cables, where the mean is 2000, standard deviation is 100.
02:23
We are taking a sample of 20 cables, and the distribution of the sample means will also be approximately normally distributed with the mean of 2000 and the standard deviation, or what they call a standard error, of the standard deviation of the original distribution divided by the square root of your sample size.
02:44
So reaching for the calculator, 100 divided by the square root of 20, is 22 .36.
02:56
So the distribution of our sample means is approximately normally distributed with the mean of 2 ,000 and the standard error of 22 .36...