00:01
In this question we are told the mean television viewing time for americans is 15 hours per week.
00:06
So there's our population mean, 15.
00:09
We also know the population standard deviation is 5.
00:13
So sigma is 5.
00:15
We're looking at samples of size 80.
00:18
So n is 80.
00:21
Okay, so i don't know the shape of the original distribution, but i do know that if i were to take every possible sample of size 80 from this population, find the sample means and plot them out, i would get something approximately normal because of the central limit theorem, which states that as sample size increases, the sample means become more and more normally distributed.
00:46
If n is at least 30, we can treat this as approximately normal.
00:50
Its mean, mean of the means, is the same as the population mean.
00:54
The standard deviation of sample means, the standard error, is sigma over root n.
01:02
So 5 over root 80.
01:06
Okay, so normal distribution question.
01:10
It wants us to round our z -scores to two decimal places, which is going to lose us some accuracy, but we'll do what they say.
01:19
The first part, part a, we want the probability the sample mean is within an hour.
01:27
Okay, so i'll draw a couple of lines on here.
01:31
14 to 16.
01:33
If the sample mean falls into this bit, then it's within an hour.
01:39
I need to get the z -score corresponding to these though.
01:42
Z is x minus mu over sigma.
01:45
Not these, i'm using these parameters since i am looking at sample means.
01:53
These are going to have the same z -score.
01:54
Just one is positive, one is negative.
01:57
Because they are the same distance away from the mean, they'll be the same number of standard deviations away from the mean.
02:05
So you want one divided by the standard error...