00:01
We are looking at a normal distribution here.
00:03
Let's draw it out.
00:09
The mean, mu, is 19, standard deviation, sigma equals 10.
00:15
For our first question, part a, we won't be probability that x is less than or equal to 1.
00:21
So 1 is below the mean, down here.
00:24
We won't be area to the left of it.
00:26
How do we work that out? well, we need to get the z score.
00:29
To get the z score, we have z equals x minus mu over sigma.
00:36
So z is 1 minus 19 divided by 10.
00:41
So that's going to be minus 1 .8.
00:47
How do we get the probability here? well, we're going to look at a z score table because it's been recommended to us.
00:55
So we go to our z score table.
00:57
What does it say? well, it gives us the distance to the mean.
01:01
It gives us this here, which isn't what we're looking for.
01:04
But i know that the total area under a normal curve is one.
01:07
And it's 0 .5 to the left of the mean, 0 .5 to the right.
01:11
So if i get this and i take it away from 0 .5, i'll be left with this little green area that we're looking for.
01:18
So, 0 .5, and i'm looking for 1 .8 in my table.
01:25
So 1 .8 is associated with the probability 0 .4641.
01:34
So i perform this subtraction to get this answer here to 4 decimal places.
01:46
Okay, for part b.
01:48
We want the probability, but x is less than 3.
01:53
So let's say this as 3 now.
01:55
Same idea as before.
01:58
Z is equal to 3 minus 19 divided by 10.
02:05
So that's minus 1 .6.
02:10
And exactly as before, i go to my z score table.
02:16
I'm looking for 1 .6, and it's 0 .44 .2.
02:24
So this is this area in black here.
02:26
So i take that away from 0 .5 .5 .8.
02:40
Oops, that's...
02:41
X is more than 3.
02:42
Whoops, that's okay though.
02:43
It's very easy to correct.
02:45
If this is the probability that x is less than 3, the probability for x is more than 3 is just 1 minus this.
02:54
So that's 0 .9 ,452.
02:58
So this is the correct answer to this bit.
03:03
Let's see.
03:04
We want the probability that it's x is between 5 and 17.
03:09
So 17 is below the mean as well.
03:12
So now instead of looking for this whole green area down here, we're looking for this interval...