00:01
A manufacturer claims their brand of hot dogs has a mean fat content, so mu, population mean, of 18 grams with a standard deviation, sigma, of 1 gram.
00:11
We're going to look at a sample of 40 hot dogs.
00:15
Okay, so we want the probability the sample mean, x -bar, is greater than 18 .25.
00:24
We are not given the shape of the population distribution, but even so, i know if i take every possible sample of size 40, take the means, and plot them out, i get something approximately normal.
00:40
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.
00:50
If n is at least 30, you can treat them as approximately normal.
00:54
The mean of the means is the same as the population mean.
00:58
The standard deviation of the sample means, or standard error, is sigma over root n, so 1 over root 40.
01:05
So we have a normal distribution question.
01:09
Our value is above the mean, and we want greater than, area to the right.
01:15
To find this, you need something with the normal distribution already built in.
01:19
The function you would have to integrate to do this by hand is far too complicated, so you could use software like excel or r.
01:27
I'm going to use my ti -84 calculator with the normal cdf function.
01:33
This has four inputs, lower bound, upper bound, mean, and standard deviation.
01:39
We're using these parameters since we are looking at a sample mean.
01:42
18 .25 is my lower bound...