00:01
Hi, i'm david and i'm here to have you answer your question.
00:04
Now let me bring up your question here.
00:07
In this question here we're going to discuss about the normal distribution.
00:13
Let me remind you that if the n greater equal to 30 and by center limit theorem, the x -par, which is a symbol mean, it will follow by the normal with the mean with the x -par equal to the mean on the population, standard division of the x -par equal to the standard division of the population of square of n.
00:36
Now we have the amount of the regular and loaded petroleum zoned, so x will be the petroleum zoned, followed by the sum distribution window mean equal to 4 ,600, standard division equal to 1000.
01:03
Now at the start here we have 7 ,400 liter and then every day there is a deliver of the 4 ,700 every day the deliver of the plus 4 ,700 and then we assume that the daily stock is only greater than the daily demand and then we want to to form from here the amount of the petroleum in the stock.
01:53
So it have at the beginning will be 700, 7 ,400.
01:58
And then every day we will have to sell under minus x amount, but there is the deliver of those 4 ,700.
02:11
And then this on every day.
02:12
So i will call it as the this one will be if we consider for the 100 days so if we consider 100 day and then this will be at the beginning we have there and then we will have minus x1 plus x2 will be the first day the second day plus up to the x 100 day and then for each day we will have the the deliver of the 4 ,700.
02:48
So we plus the 100 times 4 ,700.
02:53
So if we simplify this one, we will see that we have the 100 times 4 ,700.
03:01
We plus with the initial one we have here, equal to the 4 ,477 ,400 minus the x1 plus x1 plus x2 plus up to the x100.
03:18
And we want to find the probability in part a, that after 100 days inclusive, the stock of petroleum and this petrol station will be below 2000.
03:32
So once you have this probability, this amount here will be smaller than 2000.
03:38
So for 77400 minus x1 up to the x100.
03:46
This one will be smaller than the 2000.
03:50
That exactly the probability we're looking for.
03:54
Now, if we've tried to simplify this one, it will be the same as the...
03:59
I will bring this one to the right -hand side, this one to the left -hand side.
04:03
So i should have this one will be the x1 plus up to the x -100 will be greater than...
04:10
If we minus 2 ,000, it should be 4 -7 -5 -400.
04:17
And this probability can be converted into the sample mean by defining everything by a hundred.
04:26
So if we do that, we should have equal to the probability of the x bar here on the left -hand side.
04:33
On the right -hand side, we divide by a hundred, so we have the four, seven, five, four.
04:39
And that will be the probability we're looking for.
04:42
Now because here by central limit theorem, we have n equal to a hundred.
04:47
Hundred is greater than 30.
04:51
So therefore we can use the central limit theorem here.
04:54
Remarge you that it will turn the x -par minus the mean with x -par of a standard division of the x -bar, it will follow by the standard normal.
05:02
It means that we need to convert the x -bite into the z.
05:06
To do that, we have to take the 4754.
05:10
We minus the mean here, dividing by the standard division on the x -bar, which is the 1 ,000 square root on the end...