00:01
So we have a normal distribution.
00:03
Let's draw that bell -shaped curve, and we know that the mean of that distribution is 400 with a standard deviation of 10.
00:09
So let's just go out and draw a few standard deviations out.
00:16
Usually we don't go out more than three.
00:19
I'm only going to go out two, but we want to find in part a, what is the area between area between 415 and the mean of 415? and so that's the same thing as finding the probability of randomly selecting a value from 400 and 415.
00:41
And so we know that this value has a z value of 0.
00:49
And this value is right here in the picture.
00:53
And that's halfway between these two.
00:55
And this is a z score of 1 and this is z score of 2.
00:57
So this is a z score of 1 .5.
01:00
And so we can find that area between.
01:03
By looking up the value of the area below 1 .5 and that corresponds with 0 .9332 and then find the area below 0 ,0, which is 0 .5, and that will give us that area between.
01:19
And so we have 0 .4332...