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As we briefly showed before, when finding the probability of rolling an average
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of at least three with the tetrahedral die, the central limit theorem is not
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only awesome, but important, because it allows us to know where any sample mean
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falls on the distribution of sample means. In the example of the tetrahedral
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die, we wanted to know the probability of getting at least a three, for an
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average, if we rolled it twice. And we found that when we looked at the
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histogram, rolling at least a 3 was 6 out of 16. And now, we're extending this
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concept to populations. So, if we have the distribution of sample means where
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the samples can be any size. Where does a particular sample mean of that same
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size fall on the distribution? If we know where it falls on the distribution,
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then we can decide if this sample is typical or if something weird is going on.
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So, let's use another example.