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We can do the same with normal distributions. Which are modeled by a special
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probability density function. We're not going to go over the equation for this
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probability function in this course, but if you want, you can easily look it up
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and see what it is. And that might be pretty cool for some of you that wants a
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little bit more information. But basically, since we have this theoretical
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curve, we can model it with an equation. And then, using this equation, we can
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use calculus to find the area under the curve. But we don't need to use
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calculus, because someone else already did, and then they created a special
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table so that we can always figure out the area under the curve between any two
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values. We're going to use this table later first let's make sure we're all up
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to speed on the normal probablity density function and the area underneath.
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First the tails never actually touch the X axis they get closer and closer to
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the X axis so the X axis a horizontal axis. [unknown] the reason the tails of
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this theoretical model don't touch the x axis is basically because we can never
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be 100% sure of anything, in other words we could have a value way out here
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really far from the mean like five standard deviations away But the probability
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of getting this value or lower is very small. And it's equal to the area under
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the curve. So if we could zoom in, we would see this tail get closer and closer
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to the x axis but never touching And then the area in between the tail and the x
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axis all the way to negative infinte is the probability of getting this value or
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lower. We'll go more into depth in that in a second. And similary we could get a
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value way out here But the probability is very small so basically what you have
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to remember is that if we have certain value let's just call it X for now that
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the area under the curve from negative infinity to X is equal to the probably of
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randomly selecting a subject in our sample less than X and this equal the
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proportion in the sample of population. With scores less than x. If this is a
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little confusing, don't worry. That's the whole point of this lesson. You're
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going to get really comfortable with using the probability density functions and
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analyzing this area, and finding this area.