[Script Info]
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Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.01,0:00:04.87,Default,,0000,0000,0000,,We can do the same with normal distributions. Which are modeled by a special
Dialogue: 0,0:00:04.87,0:00:10.01,Default,,0000,0000,0000,,probability density function. We're not going to go over the equation for this
Dialogue: 0,0:00:10.01,0:00:15.08,Default,,0000,0000,0000,,probability function in this course, but if you want, you can easily look it up
Dialogue: 0,0:00:15.08,0:00:19.63,Default,,0000,0000,0000,,and see what it is. And that might be pretty cool for some of you that wants a
Dialogue: 0,0:00:19.63,0:00:24.01,Default,,0000,0000,0000,,little bit more information. But basically, since we have this theoretical
Dialogue: 0,0:00:24.01,0:00:28.38,Default,,0000,0000,0000,,curve, we can model it with an equation. And then, using this equation, we can
Dialogue: 0,0:00:28.38,0:00:32.31,Default,,0000,0000,0000,,use calculus to find the area under the curve. But we don't need to use
Dialogue: 0,0:00:32.31,0:00:36.66,Default,,0000,0000,0000,,calculus, because someone else already did, and then they created a special
Dialogue: 0,0:00:36.66,0:00:41.02,Default,,0000,0000,0000,,table so that we can always figure out the area under the curve between any two
Dialogue: 0,0:00:41.02,0:00:46.50,Default,,0000,0000,0000,,values. We're going to use this table later first let's make sure we're all up
Dialogue: 0,0:00:46.50,0:00:52.06,Default,,0000,0000,0000,,to speed on the normal probablity density function and the area underneath.
Dialogue: 0,0:00:52.06,0:00:57.54,Default,,0000,0000,0000,,First the tails never actually touch the X axis they get closer and closer to
Dialogue: 0,0:00:57.54,0:01:03.23,Default,,0000,0000,0000,,the X axis so the X axis a horizontal axis. [unknown] the reason the tails of
Dialogue: 0,0:01:03.23,0:01:09.24,Default,,0000,0000,0000,,this theoretical model don't touch the x axis is basically because we can never
Dialogue: 0,0:01:09.24,0:01:14.70,Default,,0000,0000,0000,,be 100% sure of anything, in other words we could have a value way out here
Dialogue: 0,0:01:14.70,0:01:20.79,Default,,0000,0000,0000,,really far from the mean like five standard deviations away But the probability
Dialogue: 0,0:01:20.79,0:01:26.84,Default,,0000,0000,0000,,of getting this value or lower is very small. And it's equal to the area under
Dialogue: 0,0:01:26.84,0:01:33.08,Default,,0000,0000,0000,,the curve. So if we could zoom in, we would see this tail get closer and closer
Dialogue: 0,0:01:33.08,0:01:39.31,Default,,0000,0000,0000,,to the x axis but never touching And then the area in between the tail and the x
Dialogue: 0,0:01:39.31,0:01:45.85,Default,,0000,0000,0000,,axis all the way to negative infinte is the probability of getting this value or
Dialogue: 0,0:01:45.85,0:01:52.41,Default,,0000,0000,0000,,lower. We'll go more into depth in that in a second. And similary we could get a
Dialogue: 0,0:01:52.41,0:01:58.58,Default,,0000,0000,0000,,value way out here But the probability is very small so basically what you have
Dialogue: 0,0:01:58.58,0:02:04.47,Default,,0000,0000,0000,,to remember is that if we have certain value let's just call it X for now that
Dialogue: 0,0:02:04.47,0:02:10.65,Default,,0000,0000,0000,,the area under the curve from negative infinity to X is equal to the probably of
Dialogue: 0,0:02:10.65,0:02:16.35,Default,,0000,0000,0000,,randomly selecting a subject in our sample less than X and this equal the
Dialogue: 0,0:02:16.35,0:02:22.06,Default,,0000,0000,0000,,proportion in the sample of population. With scores less than x. If this is a
Dialogue: 0,0:02:22.06,0:02:27.09,Default,,0000,0000,0000,,little confusing, don't worry. That's the whole point of this lesson. You're
Dialogue: 0,0:02:27.09,0:02:32.26,Default,,0000,0000,0000,,going to get really comfortable with using the probability density functions and
Dialogue: 0,0:02:32.26,0:02:35.13,Default,,0000,0000,0000,,analyzing this area, and finding this area.