00:01
So we have two normal distributions.
00:02
We have, first of all, we have andrea, and i'll just call her and.
00:09
And she has a normal distribution for finishing this race of 62 seconds and a standard deviation of 0 .8 seconds.
00:18
And then we have the distribution.
00:21
Sorry, that is like ever so crooked.
00:23
We got to start that over.
00:24
Then we have ashley, and we'll just call her ash.
00:28
And ashley has a mean time that is 62 .8 seconds and a standard deviation of one second.
00:43
And then we'll have another distribution, and that is going to be the distribution of having ashley's time minus andrea's time.
00:56
And that should center at the difference between those two of ashley minus the mean for ashley minus the mean for this.
01:08
We would assume that mean if we take that difference, we're going to get that that difference is 0 .8 seconds.
01:15
And the standard deviation for that distribution of ashley minus andrea will end up equaling that square root of and we would take the variance squared plus the variance squared and square rooted to give our standard deviation for that difference distribution.
01:41
And so our first question is, what's the likelihood that andrea, the time of andrea, is less than 60 seconds? and so we can see 60 seconds is maybe about here on her scale, and we need to find that probability.
02:02
So let's convert it to a z value.
02:04
Now we have 60 minus 62 divided by 0 .8 or negative 2 divided by 0 .8 gives us a z value of negative 2 .5.
02:18
And the area below negative 2 .5 is 0 .00 .5...