00:01
So we're looking at a normal distribution.
00:02
I'm going to start by drawing it.
00:06
There we go.
00:08
And we don't know the mean, we don't know the standard deviation.
00:11
We want to find those.
00:13
But we do have some information.
00:15
So if i mark on here 7 and 12, these represent the middle 20%.
00:22
So this area in between is 20%, 0 .2.
00:31
So that leaves the other 80 % in the tails.
00:34
So each tail represents 40%, 0 .4.
00:39
Because when we say middle 20%, we mean it's symmetric.
00:43
So we are dealing with some symmetry here.
00:46
So we have this.
00:47
How do we turn that into a mean and standard deviation? well, i'm going to find the z -scores corresponding to these two values.
00:56
Z tells you how many standard deviations away from a mean a value is.
01:01
So if we start with 7, to get the z -score, i'm going to use excel with the inverse normal function.
01:11
You just put an area, capital a, in.
01:15
And that's the cumulative area, so area to the left.
01:18
So for 7, we put in 0 .4 and get z is minus 0 .25335...