00:01
In this question, we are looking at a normal distribution.
00:04
So i'm going to start by drawing it.
00:08
So the normal distribution has an area underneath the curve of 1.
00:13
It's a probability curve.
00:14
And it is symmetric.
00:16
So the area to the left of the mean is 0 .5.
00:19
To the right of the mean is also 0 .5.
00:22
For part a, we want to know what proportion of newborn boys have a head circumference larger than 35.
00:29
So the mean, mu, is 34 .5 centimeters.
00:34
Standard deviation, sigma, is 1 .27.
00:37
So 35 is above the mean, and we want to know what proportion land here, larger than 35.
00:48
So would be normal distribution.
00:49
We don't use raw values, we use z scores.
00:53
Z is x minus mu over sigma.
00:58
So here we have 0 .5 divided by 1 .5.
01:04
Which is probably, yep, i'm just going to stick with the exact value.
01:08
I don't want to get any rounding errors from this.
01:12
This tells me how many standard deviations away from a mean the value is.
01:16
Now i need to turn it into probability.
01:19
And to do that, you need either your graphical calculator or software like excel.
01:24
You can use a z score table, but it will give you less accuracy because you have to round the z score to use the table.
01:31
So i'm going to use technology.
01:32
There are two types of table or two functions you can use.
01:37
They'll be standard and the cumulative normal functions.
01:41
The standard gives you the area between x and mu.
01:48
So if you put this in, you get this area here, which would be very, very useful for part b, but here not exactly what we want.
01:56
So if you take this red area away from 0 .5, you do get the answer to part a.
02:02
Cumulative is the area to the left.
02:08
Everything we don't want.
02:09
Take it away from one, you get the areas for the right.
02:15
So for part a i'll use the standard function.
02:18
So i need 0 .5 minus whatever i get.
02:21
I put this in to get 0 .1531.
02:26
So my answer is 0 .3469.
02:34
We get that back.
02:36
For part b, we want the probability or rather the proportion between 34.
02:45
So now we want this area, which we get by just putting this into the standard function.
02:51
It's 0 .1531.
02:56
But see, we want to know the cutoff point for the third percentile.
03:02
So that's going to be way down here, e3...