00:01
We're looking at a normal distribution.
00:03
We actually have two normal distributions, but i'm going to use one image for each of them and just change where the cutoff points are.
00:12
So for part a, the mean, mu, is 10, and the standard deviation, which i'll put as sigma, is 5.
00:21
So this midpoint here is 10.
00:23
What's the probability of taking a value between 10 and 20? so here's 10.
00:29
Let's mark 20 on here as well.
00:31
We want to know the probability of falling into this area.
00:35
So that's going to be the same as the value of this area.
00:40
If we find this area, that is also the probability, a random variable will fall into that.
00:46
So how do we find this area? well, with the normal distribution, we don't use raw values.
00:51
We standardize it to a z score.
00:54
So we take this and we look for the z score.
00:58
And z is equal to x minus mu over sigma.
01:02
So here we have 20 minus 10 over 5, which is 2.
01:08
The other z score is for 10, which is 0.
01:13
So this is telling us that 20 is two standard deviations above the mean.
01:18
And now i have a z score, i can use the standard normal curve to find this probability.
01:24
And the normal functions are complicated.
01:26
We don't do it by hand.
01:28
You need to find something that already has the normal function calculated for you.
01:32
This could be a z score table, it could be a graphical calculator, it could be software like excel.
01:39
And for all of these, there are two types of table or two functions.
01:43
They're called the standard and the cumulative.
01:48
So if you put two into the standard function, it will give you the area between your cutoff point, mu, your cutoff point x rather, x and mu.
02:01
So if you put into, it gives you this area.
02:03
In this case, that's exactly what we want, so that's great.
02:07
Cumulative gives you the area to the left.
02:12
So if you put in two, it would give you all of this.
02:15
Not quite what you want, but the curve is symmetric.
02:18
The area to the left of the mean, all of this, is 0 .5...