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Showing Revision 1 created 02/27/2013 by Cogi-Admin.

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