00:02
To calculate the probability that the average for our 59 cars lands between 28 .9 and 29 .6, we need to apply the central limit theorem, which says if we repeatedly took samples of 59 cars and calculated all their averages, the samples would form a bell curve centered at the population average of 29, and the standard deviation of all of our little samples is calculated by the population standard deviation for, divided by the square root of our sample size 59.
00:36
So that's going to give us a standard error of .52.
00:43
So i'm going to number my bell curve to the right and to the left by .52 to get us a picture of what's happening.
00:52
And now let's mark where 28 .9 and 29 .6 fall.
00:57
28 .9 would land right about here and 29 .6 would land right about here and 29 .6 would land right about here.
01:05
And what we want to know is the area in between these two markers.
01:10
So to do that, we're going to need a z score for each one of those values.
01:14
So let's start with the low one, 28 .9 minus the mean divided by our standard deviation is going to be negative 0 .1 divided by 0 .52, which is a z score of negative 0 .19.
01:35
Now let's reference...