
We can do the same with normal distributions. Which are modeled by a special

probability density function. We're not going to go over the equation for this

probability function in this course, but if you want, you can easily look it up

and see what it is. And that might be pretty cool for some of you that wants a

little bit more information. But basically, since we have this theoretical

curve, we can model it with an equation. And then, using this equation, we can

use calculus to find the area under the curve. But we don't need to use

calculus, because someone else already did, and then they created a special

table so that we can always figure out the area under the curve between any two

values. We're going to use this table later first let's make sure we're all up

to speed on the normal probablity density function and the area underneath.

First the tails never actually touch the X axis they get closer and closer to

the X axis so the X axis a horizontal axis. [unknown] the reason the tails of

this theoretical model don't touch the x axis is basically because we can never

be 100% sure of anything, in other words we could have a value way out here

really far from the mean like five standard deviations away But the probability

of getting this value or lower is very small. And it's equal to the area under

the curve. So if we could zoom in, we would see this tail get closer and closer

to the x axis but never touching And then the area in between the tail and the x

axis all the way to negative infinte is the probability of getting this value or

lower. We'll go more into depth in that in a second. And similary we could get a

value way out here But the probability is very small so basically what you have

to remember is that if we have certain value let's just call it X for now that

the area under the curve from negative infinity to X is equal to the probably of

randomly selecting a subject in our sample less than X and this equal the

proportion in the sample of population. With scores less than x. If this is a

little confusing, don't worry. That's the whole point of this lesson. You're

going to get really comfortable with using the probability density functions and

analyzing this area, and finding this area.