﻿[Script Info] Title: [Events] Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text Dialogue: 0,0:00:00.29,0:00:05.11,Default,,0000,0000,0000,,As we briefly showed before, when finding the probability of rolling an average Dialogue: 0,0:00:05.11,0:00:09.65,Default,,0000,0000,0000,,of at least three with the tetrahedral die, the central limit theorem is not Dialogue: 0,0:00:09.65,0:00:14.40,Default,,0000,0000,0000,,only awesome, but important, because it allows us to know where any sample mean Dialogue: 0,0:00:14.40,0:00:19.84,Default,,0000,0000,0000,,falls on the distribution of sample means. In the example of the tetrahedral Dialogue: 0,0:00:19.84,0:00:25.48,Default,,0000,0000,0000,,die, we wanted to know the probability of getting at least a three, for an Dialogue: 0,0:00:25.48,0:00:31.04,Default,,0000,0000,0000,,average, if we rolled it twice. And we found that when we looked at the Dialogue: 0,0:00:31.04,0:00:36.40,Default,,0000,0000,0000,,histogram, rolling at least a 3 was 6 out of 16. And now, we're extending this Dialogue: 0,0:00:36.40,0:00:42.29,Default,,0000,0000,0000,,concept to populations. So, if we have the distribution of sample means where Dialogue: 0,0:00:42.29,0:00:47.58,Default,,0000,0000,0000,,the samples can be any size. Where does a particular sample mean of that same Dialogue: 0,0:00:47.58,0:00:52.95,Default,,0000,0000,0000,,size fall on the distribution? If we know where it falls on the distribution, Dialogue: 0,0:00:52.95,0:00:58.14,Default,,0000,0000,0000,,then we can decide if this sample is typical or if something weird is going on. Dialogue: 0,0:00:58.14,0:01:00.63,Default,,0000,0000,0000,,So, let's use another example.