00:01
A test of mathematical skill is normally distributed.
00:05
Okay, so let's start by drawing this.
00:09
I have a normal distribution.
00:12
My mean, mu, is 90, standard deviation, sigma is 13.
00:17
A student gets a score of 101.
00:20
So that's above the mean.
00:21
What percentage of students does she do better than? so that's going to be what percentage is to her left? what percentage did scored worse than her.
00:34
So with a normal distribution, we like to use z scores rather than raw data, and z is equal to x minus mu over sigma.
00:44
So here, we have 101 minus 19, minus 90, divided by 13, which is 0 .862.
00:56
So the z score tells you how many standard deviation away from the mean a value is.
01:03
So this cutoff point is 0 .85 standard deviations above the mean.
01:08
So the answer is not part a.
01:10
In fact, looking at this, based on that, i'm going to say the answer is part d because this is clearly more than half the curve.
01:20
And the total area under the curve is 1, half to the left, half to the right of the mean.
01:25
So this is definitely not 0 .2 or 0 .15.
01:28
So the answer is going to be d.
01:30
But anyway, how do we get from z score to probability? well, you need either a z score table, a graphical calculator, or some kind of software like excel.
01:41
And there are two functions you might use.
01:44
The standard and the cumulative, or two types of table.
01:48
The standard table, or standard function, when you put in your z score, gives you this area here.
01:54
Between your cutoff and the mean.
01:56
Not entirely what you want.
01:58
You have to add 0 .5 for the rest of the number.
02:01
Of the curve and then you'll have your answer.
02:04
The cumulative function gives you the area to the left, so it just gives you the answer immediately.
02:10
So i'll take my z score, go to the cumulative function, and it is 0 .8013 if i use the z score saved in my calculator.
02:21
If i just use 0 .8462, i still get it.
02:35
I get 0 .25...