00:01
All right, so we have a t -distribution with 18 degrees of freedom and we're going to find the area probability, area or probability, in each of these regions.
00:08
So our t -distribution is approximately normal, so i'm going to draw an approximately normal curve.
00:13
T -score of zero is right in the center.
00:15
Here it is approximately in the center.
00:18
And this is, any time you're doing stuff with a z -distribution or a t -distribution or some kind of, any rounded distribution, it's really good to draw it to get an understanding of what's going on.
00:26
So here's the t -distribution and degrees of freedom is 18.
00:31
And we want to find the area for a.
00:33
We want to find the area to the right of 1 .734.
00:37
So 1 .734 is going to be roughly here.
00:42
The area to the right of it is this.
00:45
And so i use the t -dist function in my spreadsheet, put in this value, 18 degrees of freedom, and one tail.
00:52
We want one tail here.
00:53
That's an important thing to note, one tail.
00:55
So again, the formula goes like this, or the parameters go like this, t -dist.
01:00
You put the absolute value of your t -score, that's going to be important in a second, the degrees of freedom, and then you have the number of tails.
01:10
So one tail because we're looking strictly up here.
01:14
Great.
01:15
And so it's 0 .05.
01:17
Good.
01:18
Now, the next part, we're going to find to the left of 2 .55.
01:21
So that's going to be, or 2 .552, i should say.
01:30
So that's everything to the left of, so it's all this stuff.
01:34
So if we use the formula, this function gives you everything above the positive value, to the right of the positive value.
01:43
But we want the left.
01:44
So what we have to do, 0 .01, that's the area to the right.
01:49
We want the area to the left.
01:50
So we do one minus that value to get the area to the right.
01:53
So 0 .989, we could probably round that to three decimals.
01:59
That's a tall order to round it.
02:01
That's going to be one to three decimal places right there.
02:03
That's pretty good.
02:08
But you'd round this.
02:09
Here's what you do.
02:10
You'd round this to three decimals, and then you do one minus 0 .1, 0 .010, and that's going to give you 0 .99.
02:29
So we'll just say 0 .99 for that.
02:34
All right.
02:36
Now, c asks us to find to the left of negative 2 .1.
02:41
Negative 2 .101...