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