00:01
Right now we're working with density curves, and we're using a key fact that when we have a density curve, the area between two points under this curve is the same as the percentage of all outcomes that lie between those points.
00:23
So the percentage of all outcomes where our random variable x is greater than a, but less than b.
00:34
So we want to take a look at something a little bit different.
00:38
Now we're given the fact that if we have some distribution curve, i'll draw it in blue here, we're told that between the points 15 and 20, the area here, and i'm shading in red, is equal to 0 .414.
01:08
So that's the area of that section of the curve.
01:11
Now, the question wants us to answer, what percentage of all outcomes are going to be outside of this range? so what percent of all outcomes are going to be less than 15 or greater than 20? well, we know from what we just said, that the percentage of all outcomes is the same thing as area under the curve in that specific range.
01:37
So since we're looking for a percentage of all outcomes less than 15, we're looking at the area under the curve to the left of 15.
01:46
And we also want to know the percentage of all outcomes greater than 20.
01:50
So we're looking for the area to the right of 20 under that curve...