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I want to show you what a normal distribution is all
about in statistics.
And there are three things that should come to mind when
you read the words normal distribution.
The first thing is that you have what's called a
bell-shaped curve.
That basically looks like this right here.
It's a bell-shaped curve.
That means that the mean, which is kind of sitting right
here in the middle, has the most data that's sitting
around on either side of the mean.
I'll talk a little more about that later.
But definitely bell-shaped curve is one of the first
things that should come to mind when you
read that word normal.
The second thing that should come to mind when you hear it,
normal distribution, is that the total area, total area
under the curve, is equal to 1.
So all of this area underneath this bell-shaped curve, all of
it including everything out here in the tails as they get
smaller and smaller, is a total area of 1.
And there's one more thing.
The third thing that should come to mind is that this
bell-shaped picture here is symmetrical.
It's symmetrical.
And that comes into play and is very handy.
It's kind of a geometric term for later problems.
So if I was to split this thing right down the center
here, you would see that half of this picture over here--
if the whole thing is 1--
is 0.5, and the other half is 0.5 giving you a total area.
Everything from here all the way over to here--
total area all together, everything
under the curve here--
gives you the total area of 1.
So those three things should come to mind when you hear the
words normal distribution--
bell-shaped, total area is 1, and it's symmetrical.
Let me just go one more step and show you what I mean by,
perhaps you've seen this as well, not only are we talking
about now a normal distribution but something
called a standard normal distribution.
So a normal distribution again are these three things--
bell-shaped, total area is 1, and symmetrical.
Standard normal kind of uses these three things but kicked
up one more notch and two other things-- we'll mark them
4 and 5, how's that.
Two other things should come to mind when that word
standard is used.
Two other things should come to mind.
Number one is that the mean and that letter-- that Greek
letter is mu which stands for population mean or population
average, same thing--
that the mean is going to be is 0.
That's what standard means.
Standard means that the mean, population mean, is 0.
And the other thing that it means is that this Greek
symbol sigma, which is lowercase sigma, and that
means population standard deviation is automatically 1.
So these two things are also part of what the standard
normal distribution.
So there's normal distribution which means these three
things-- we covered those a second ago.
But when you read the words standard normal, these two
things also come into play.
Which means, going back to this picture here, that the
mean, sits right here in the middle, is 0.
The average is going to be 0.
And that 1 standard deviation, 1 standard deviation in either
direction, is also into play.
So that's what we mean.
And there's this other idea called the empirical rule, but
we can get into that another time.
That's 68% of your data sitting smack within one
standard deviation.
But this is just a real rudimentary level of what we
mean by a standard normal--
means that the population mean is 0, population standard
deviation is 1.
And when we say normal, we mean it's bell-shaped, total
area is 1, and it's symmetrical.
Hope that helps.