1 00:00:00,290 --> 00:00:05,114 As we briefly showed before, when finding the probability of rolling an average 2 00:00:05,114 --> 00:00:09,650 of at least three with the tetrahedral die, the central limit theorem is not 3 00:00:09,650 --> 00:00:14,402 only awesome, but important, because it allows us to know where any sample mean 4 00:00:14,402 --> 00:00:19,842 falls on the distribution of sample means. In the example of the tetrahedral 5 00:00:19,842 --> 00:00:25,482 die, we wanted to know the probability of getting at least a three, for an 6 00:00:25,482 --> 00:00:31,037 average, if we rolled it twice. And we found that when we looked at the 7 00:00:31,037 --> 00:00:36,400 histogram, rolling at least a 3 was 6 out of 16. And now, we're extending this 8 00:00:36,400 --> 00:00:42,290 concept to populations. So, if we have the distribution of sample means where 9 00:00:42,290 --> 00:00:47,580 the samples can be any size. Where does a particular sample mean of that same 10 00:00:47,580 --> 00:00:52,948 size fall on the distribution? If we know where it falls on the distribution, 11 00:00:52,948 --> 00:00:58,140 then we can decide if this sample is typical or if something weird is going on. 12 00:00:58,140 --> 00:01:00,633 So, let's use another example.