00:03
Okay, so we have a mound shape symmetrical distribution that looks something like this, and we have a mean of 100 and a 16th percentile of 85.
00:14
Okay, and it says to use the empirical rule, which is a name for the 68, 95, 99 .7 rule.
00:32
Okay, and that's because one standard deviation contains, on either side contains 68 % of the data.
00:39
Two standard deviations is 95 and 3 is 99 .7.
00:44
Okay, so it tells me the means 100.
00:48
Mean goes in the middle.
00:51
16th percentile.
00:54
So this is how we're going to go about this.
01:00
68 % is from here to here.
01:02
That means on either side is 34%.
01:09
So what about these gray areas? well, if i take 95 and subtract 68 and then divide in half, i can know what from here to here equals.
01:32
Or, better yet, let's take the 100 % minus 68.
01:45
Actually, no, i'm making it more complicated than it needs to me.
01:49
This one's 34 half of it is 50 right so from here all the way to the end is half the data the means right in the middle so if i do 50 % minus 34 % that gives me 16%.
02:09
So that means the 16th percentile equals 85 85 is right here that's my 16th percentile that also means, since it folds in half and is symmetric, that 115 would go right there.
02:30
How do i know that? well, we'll talk about that in a second.
02:36
So 85 is that.
02:39
And then how do i know the standard deviation? 100 minus 85 means the standard deviation is probably about 15, which is how i got to 115 for the other side.
02:56
Which is the 84th percentile.
03:08
Because that means from here down is 16%.
03:16
From here down, all the way down, is 68 plus 16, which equals 84.
03:34
All right.
03:35
Now we need a z score for 90.
03:39
Well, you find the z score, by doing the data point minus the mean divided by the standard deviation.
03:57
And this is going to equal negative 0 .67.
04:04
And we need the percentile for 160.
04:10
Well, let's do some more of these.
04:21
130, 145, and 160 is going to be four standard deviations away.
04:26
That's going to be really, really rare.
04:29
It's going to be an outwire.
04:31
So the percentile, remember, is everything below it, so it basically has everything.
04:39
So the percentile is definitely going to be the 99th percentile, because we actually don't have an 100 percent.
04:47
We don't do 100 percent tile.
04:52
Are you going to have many scores below 35? let's see here.
04:58
So let's subtract 15.
05:03
And subtract 15.
05:08
Oh, this will be 55.
05:11
Wow.
05:12
35 is going to be clear down here.
05:16
So are there many scores below 35? no.
05:21
Probably not any.
05:23
And so the score 35 is more than three standard deviations below the mean.
05:34
Oh, crap.
05:36
I wrote down the wrong mean.
05:38
That changes everything.
05:40
Thing.
05:42
I'm sorry.
05:52
Okay.
05:52
So that means our standard deviation is wrong.
05:56
I'm so sorry.
05:57
This was so much easier a second ago.
06:02
Okay.
06:03
110 minus 85 is 25...