00:01
We're looking at a normal distribution here.
00:02
I'm going to start by drawing it.
00:05
So normal distribution, mean mu of nine pounds, standard deviation sigma of 2 .1.
00:15
And for part a, we want the probability that a random pumpkin is at least 15 pounds.
00:21
So that's above the mean.
00:22
Let's mark on here.
00:24
And we want the area to the right.
00:26
So normal distribution.
00:28
We don't use raw data.
00:29
We standardise it into a z score.
00:31
Z is x minus mu over sigma.
00:37
So i want 15 minus 9 divided by 2 .1, which is 2 .87.
00:43
And with some more decimal places i have saved.
00:48
Now we need to turn that into probability.
00:51
So you could use a calculator, or you could use excel, or some other software, and there are two functions you might use.
00:58
Standard and cumulative.
01:01
Standard gives you the area between x and mu.
01:07
This area here.
01:09
Not quite what you want, but the total area under this curve is 1, it's a probability curve, and it's symmetric.
01:17
So this area, to the right of the mean, is 0 .5.
01:20
So take this away from 0 .5, we'll have the answer.
01:26
Cumulative gives you the area to the left.
01:31
All of this.
01:33
Also not what you want, but take that away from 1, you can.
01:36
Get the answer.
01:37
I'll use the standard.
01:38
So 0 .5 minus whatever i get by putting this into the standard function, which is 0 .497.
01:51
For an answer, 0 .0 .021.
01:58
So that's part a.
02:01
Heart b, we are no longer looking at individual pumpkins.
02:06
We're looking at a group of 30.
02:08
So this changes things.
02:10
We're looking at the average weight of a group of 30.
02:13
So we're now looking at a sampling distribution.
02:16
So we need the mean of the sample weights, the mean of the mean of the sample weights, and that's going to be the same as the original.
02:27
It's the average of the averages.
02:30
But the standard deviation of the sample means is going to be a bit different...