00:01
We're looking at a distribution.
00:02
It's bell -shaped.
00:04
Its mean is 39 ,000.
00:08
Its standard deviation is 2 ,200.
00:13
In part a, we're looking at z -scores.
00:17
Z tells you how many standard deviations away from a mean a value is.
00:21
You find it by taking the raw value, subtracting the mean, dividing by the standard deviation.
00:28
So we have 34 ,000, 36 ,000, and 32 ,000.
00:38
So for all of these, we are going to subtract 39 ,000 and then divide by 2 ,200.
00:43
So let's do that.
00:49
And i get for the first one minus 2 .27 to two decimal places.
00:59
Let me check.
00:59
Yep, nearest hundred.
01:00
Drop.
01:01
36 ,000 gives me minus 1 .36.
01:09
32 ,000 gives me minus 3 .18.
01:14
There are our z -scores.
01:16
Are there any outliers here? yes.
01:20
We consider something to be unusual or an outlier if it is more than two standard deviations away from the mean.
01:29
So if the absolute value is more than two.
01:32
So it could be more than two above, more than two below.
01:35
Part.
01:37
Now we want to use the empirical rule.
01:39
So i'll draw out a distribution here.
01:46
It's symmetric.
01:47
Total area of one or 100%.
01:49
And because it's symmetric, the mean is right in the middle here.
01:53
I'm just going to put 39 since i don't want to draw too many zeros...