00:02
We're going to be using the central limit theorem to solve this problem.
00:06
So the central limit theorem says that we repeatedly take samples of size 25 and calculate their averages.
00:14
Those averages are going to make a bell curve, as shown here, with a center right around the population mean of 106.
00:22
And then the standard deviation of all those little samples is going to be the population standard deviation, which is 12, divided by the square root.
00:32
Of our sample size, which was 25.
00:36
So essentially we're going to do 12 divided by 5, and our standard error, standard deviation 2 .4.
00:45
So now i'm going to number this bell curve by 2 .4s.
00:50
And now we want to figure out the probability that the sample mean is bigger or exceeds 110.
00:57
So notice here on my bell curve 110 is right about here.
01:01
And we want to figure out this area to the right.
01:04
That will be the same as the probability.
01:07
So we're going to need a z score for 110.
01:10
So we're going to do 110 minus the mean divided by our standard deviation of 2 .4.
01:17
And that's going to give us a z score of 1 .67...