00:01
We are told that highway drivers in a particular state travel at an average speed, so new population mean, of 61 .6 miles per hour.
00:09
Population standard deviation sigma is 5 .8, but we are not looking at individual drivers, we're looking at a sample of 30 of them.
00:18
We want the probability that the sample mean, x -bar, is less than 60.
00:25
So i don't know the shape of the population distribution, but i do know if you take every sample of size 30, take the means, plot them out, you get something approximately normal.
00:35
This is because of the central limit theorem, which states that as sample size increases, sample means become more and more normally distributed.
00:44
If n is at least 30, e treatment is approximately normal.
00:48
The mean of the means is the same as the population mean.
00:52
The standard deviation of the sample means, or standard error, is sigma over root n, so 5 .8 over root 30.
01:01
60 is below the mean, we want less than, so we want the error to the left.
01:07
At this point you need something with the normal distribution built in...