00:01
We're looking at the mean preparation fee for a particular tax form.
00:06
It's 302.
00:08
And we're given this population standard deviation of $100.
00:13
And we want the probability of a sample mean being within $16 of the population mean for varying sample sizes.
00:20
Starting with a.
00:22
N is 40.
00:24
So i don't know the shape of the original population, the fee for individual tax forms of this type.
00:30
But i do know that if i took every sample of size 40, took the means and plotted them out, i'd get something approximately normal.
00:38
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.
00:48
If n is at least 30, you can treat them as approximately normal.
00:53
The mean of the means is the same as the population mean.
00:56
So $302, regardless of sample size.
01:00
The standard deviation of the sample means, or standard error, is sigma over root n.
01:06
So in part a, the standard error is 100 over root 40.
01:13
So the mean of this distribution is 302.
01:16
I'm going to put two more values on here.
01:23
284, 380, oops, it should be 6.
01:27
Both of these values are 16 away from the population mean.
01:34
So if the sample mean falls into this area, it meets the criteria we're looking at.
01:41
So to find this area, you need something with the normal distribution built into it.
01:46
That could be software like excel or r.
01:48
I'm going to use my ti -84 calculator with the normal cdf function...