I'm going to finish off this set of

distributions by introducing what is perhaps the most important of all of

the probability distributions, and that's called the normal distribution.

Sometimes you might have heard the normal distribution referred to as

the bell curve colloquially.

Now many different processes turn out to be well

approximated by normal distributions,

and there are some mathematical reasons to not be surprised by that.

And one of those mathematical reasons is known as the Central Limit Theorem, and

it says to us that we really shouldn't be surprised to see normal distributions

around us in day-to-day life.

And so it's not a goal of this particular module to talk in

depth about the Central Limit Theorem in any way, but it's out there and

it does provide an explanation as to why we see normal distributions in practice.

Now one of the important features of the normal distribution

is that you only need to know two numbers to completely characterize it, and

those two numbers happen to be the mean mu and the standard deviation sigma.

Furthermore, a normal distribution is symmetric about its mean, so

it's one of these symmetric distributions.

So here are some examples of processes that might lend themselves to be modeled

well with normal distributions.

And so in the biological world if you go out and you measure the heights and

weights of people and start plotting those, wouldn't be at all surprised

to see something that looks a little bit like a bell curve.

If you go into the financial world and you start looking at stock returns and

you plot stock returns, then you see something in terms of a distribution,

a histogram that looks a little bell-shaped as well.

Not exactly, but it's not a bad first approximation.

If you were to give an exam and look at the scores on this exam, then it's

not unusual to see an approximate normal distribution for a set of exam scores.

And in a manufacturing process,

if we were looking at the size of a particular automotive component,

there's always a little uncertainty in any manufacturing process.

Nothing comes out exactly the same every time.

And if we were to, say, take a automotive component and

measure its width and look at a histograms of those widths,

I wouldn't be at all surprised to see a normal distribution.

So the point that I'm making here is that these normal distributions have some

universality component to them.

We see them all over the place.

And the normal distribution is a commonly used model and

if you're creating one of these Monte Carlo simulations, then it's very frequent

to make normality assumptions for the inputs, and these Bernoullian binomials

as well really lend themselves as building blocks of models.