00:01
The weight of men is normally distributed with mean mu 182 .9 pounds, standard deviation sigma 40 .8 pounds.
00:12
We aren't looking at individuals.
00:14
We have an elevator with nine people.
00:17
So we have a sample of nine, we're assuming they are randomly selected.
00:22
We want the probability that the elevator is overloaded.
00:27
So it has a limit of 1800 pounds.
00:32
If i divide that by nine, that's 200 pounds each as the average.
00:37
So the average of these people has to be below 200 pounds.
00:47
So probability, the x bar, the sample mean is less than or equal to, less than, less than or equal, it isn't actually to matter.
00:58
Because if i take every possible sample, take the sample means and plot them out, i'm just going to get another normal distribution.
01:06
The mean, mean of the means, is the same as the population mean.
01:11
Standard deviation of the sample means is sigma over, so 40 .8 over root 9, which is of course 3, is 13 .6.
01:26
And these parameters are coming from the central limit theorem, which states that as sample size increases, sample means become more and more normally distributed compared to the original distribution.
01:39
Since the original distribution here was normal, you can't get more normal than normal, so we can just leave it.
01:47
Okay, so we want 200, which is above the mean, and we need our sample mean to fall below that.
02:00
So to find the area under the curve, we need something that has the normal distribution built in, because it's too complicated to really do so.
02:09
That could be software like excel or r, or i'm going to use a ti -84 calculator with the normal cdf function...