00:01
Hi, we're looking at a problem that has to do with the area under a standard normal curve for an area in between two z values.
00:09
So just to give us a graph about that, we have a normal curve that looks like this, and our mean is in the middle.
00:18
The mean, remember, is where the z is equal to zero.
00:23
To the left, z goes negative, and to the right, z goes positive.
00:31
Usually we talk about the extremes as being like negative 3 z and positive 3 z because they have to they align with our standard deviations.
00:39
So for our four different problems here, they're pretty straightforward.
00:42
You've got to use a z table in order to find these numbers.
00:45
So for the first one, we're looking at two values when z is equal to negative 2 .04.
00:50
And on a z table, that aligns with the area under the curve of 0 .02 .07.
01:00
The second value is z equals 0 .91, and that aligns with, from the z table, 0 .8186.
01:13
So if we're looking at this on the graph, we're looking at two different places.
01:18
Negative 2 .04 is somewhere over here, and that gives us this area here, that 0207.
01:28
0207.
01:29
The 0 .816 comes on the positive side, like somewhere over here.
01:35
And this is giving us this whole area, not just in between, but also that overlap.
01:41
So in order to find the area in between this blue part, if you will, we have to subtract.
01:48
So we do 0 .816 minus 0 .027.
01:54
And that will give us the area under the curve, in between those two z values, which is 0 .7979.
02:05
Now, you're going to follow this pattern for all four of these problems.
02:10
In the second one, it's just different amounts.
02:15
So z is negative 1 .98, and z is negative 1 .28...