00:01
So we're looking at a normal distribution here, based on the amount of sodium consumed per day by the average american man.
00:09
So it's normally distributed.
00:13
We'll put this and centre it around the mean.
00:15
The mean, the average, is mu equals 9 .8 grams.
00:21
The standard deviation is sigma equals 0 .9.
00:25
We want to work out, first of all, so part b here, is the probability that they consume between 9 .4, and 10 .2.
00:36
So that's a probability, but x is between 9 .4 and 10 .2.
00:44
So how are we going to go about working this out? well, we're going to be using the normal distribution probability tables, and since we haven't been given the table, we'll just use probably a graphical calculator, because that's more exact.
00:58
So what interval are we looking at? 9 .4 is just below the mean, 10 .2 is just above it.
01:07
And one thing i notice here is both of these values are the same distance away from the mean.
01:12
So this interval is actually symmetrical.
01:17
So we could actually split into two.
01:19
These two halves on either side of the mean are going to be equal size.
01:25
Next let's work out the z scores that correspond to this.
01:28
So z is equal to x minus mu over sigma.
01:34
So let's have a look at 10 .2.
01:36
10 .2 minus 9 .8, divide by 0 .9 is 0 .4 recurring.
01:48
And because this is the same distance away from a mean, and z is a measure of how many standard deviations away from the mean, the value is, 9 .4 is just going to be minus 0 .4 recurring.
02:01
So that's our z score, and you could use a z score table, but they only go to two decimal places.
02:08
And clearly this is a transcendental number, so it would be better to use technology for this, because it will give you a more exact answer.
02:17
Now, how are we going to go about doing this? well, we could work out the area between here and the mean, and just double it, because they are going to be the same size.
02:28
Or you could work out the area to the left of 10 .2 and take away the area to the left of 9 .4, because 10 .2, below that would be red plus green.
02:42
Below 9 .4 is just red.
02:43
So if you take red plus green, subtract red, you'll be left.
02:46
Left with green.
02:47
So you can do a lot of different options as long as you respect the geometry of this area under this curve.
02:54
But let's just do the distance to the mean.
02:57
And this is what you'll see if you look at a z score table as well.
03:00
So looking at 10 .2, which is a score of 0 .4 recurring, gives us a distance to the mean of 0 .1716.
03:14
And i'm just going to label this bit here as alpha...