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← Get to Know the PDF - Intro to Descriptive Statistics

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Showing Revision 3 created 05/24/2016 by Udacity Robot.

  1. We can do the same with normal distributions, which are modeled by a special
  2. probability density function. We're not going to go over the equation for this
  3. probability density function in this course. But if you want, you can easily
  4. look it up and see what it is. And that might be pretty cool for some of you
  5. who want a little more information. But basically, since we have this
  6. theoretical curve, we can model it with an equation. And using this equation,
  7. we can use Calculus with a curve. But, we don't need to use Calculus, because
  8. someone else already did. And then, they created a special table, so we can
  9. always figure out the area under the curve between any two value. We're going
  10. to use this table later. First, let's make sure we're all up to speed on the
  11. normal probability density function and the area underneath. First, the tails
  12. never actually touch the x-axis, they get closer and closer to the x-axis. So,
  13. the x-axis is a horizontal asymptote. The reason the tails of this thoretical
  14. model don't touch the x-axis is basically because we can never be 100% sure of
  15. anything. In other words, we could have a value way out here, really far from
  16. the mean, like five standard deviations away. But the probability of getting
  17. this value or lower is very small. And it's equal to the area under the curve.
  18. So, if we could zoom in, we would see this tail get closer and closer to the
  19. x-axis but never touching. And then, the area in between the tail and the
  20. x-axis, all the way to negative infinity is the probability of getting this
  21. value or lower. We'll go more into depth in that in a second. And similarly, we
  22. could get a value way out here. But the probability is very small. So
  23. basically, what you have to remember is that if we have a certain value, let's
  24. just call it x for now. That the area under the curve from negative infinity to
  25. x is equal to the probability of randomly selecting a subject in our sample
  26. less than x. And this is equal to the proportion in the sample or population
  27. with scores less than x. If this probability is 80%, then we say x is the 80th
  28. percentile. If this probability is 90%, we say x is the 90th percentile, etc.
  29. If this is a little confusing, don't worry. That's the whole point of this
  30. lesson. You're going to get really comfortable with using the probability
  31. density functions and analyzing this area, and finding this area.