00:01
Let me take notes what's given here.
00:03
First of all, the mean value was given.
00:05
So the mean, which is denoted by mood, this is given as 50 ,000.
00:12
And the standard deviation was also given here, which is denoted by sigma.
00:18
That was given as 10 ,000.
00:21
And what about the sample size here? so the sample size was given which is 11 weeks.
00:27
So i'm going to use this n value, which is denoted by the sample size.
00:31
This is equal to 11 here.
00:33
So first of all, the starting supply is 74 ,000 gallons and the vehicle delivery is 47 ,000 gallons.
00:46
And what about for the total? so the total supply for 11 weeks, which is equal to.
00:56
So the initial supply, which is 74 ,000 and plus.
01:02
So each week, the supply is for the 7 ,000.
01:06
So we have totally 11 weeks.
01:08
I'm going to multiply the 11 by the 47 ,000, which is equal to this is 74 ,000 and plus this is 11 times 47 ,000, which is equal to this is 59 and 5991 ,000.
01:27
This is the supply, total supply for 11 week period.
01:31
So in the first part of the question, we have to supply.
01:36
Will be below 20 ,000 gallons.
01:40
And what about the difference of them? so i'm going to just first of all find the difference.
01:47
So the difference for this one, let me just write clearly.
01:50
This is difference, which is 591 ,000 and minus 20 ,000, which is equal to 571 ,000.
02:01
So therefore, we need more than this value here.
02:05
So i'm going to just define the variable x here, which is normally distributed.
02:10
This is $50 ,000, $50 ,000 gallons, and then 10 ,000 gallons, which is the distribution here.
02:17
So for the total supply, so i'm going to use the random variable t4.
02:23
So for total supply, i'm going to use the random variable as the random variable.
02:29
Let me just write as t just only.
02:32
This is the random variable we are going to use.
02:34
So the probability of the random variability, which should be greater than, which is 571 ,000.
02:42
In order to get this one, what am i supposed to? i'm going to just find the z value here.
02:47
If i just convert this value into the z value, minus the mean value.
02:51
So the mean value for 11 weeks would be this is 11 times.
02:55
So each the mean value here, which is 50 ,000, and divided by the standard division.
03:02
So for the standard division, that would be, which is the square of.
03:08
So this is square of which is 11 times the 10 ,000, which is equal to.
03:20
So what i'm going to do, i'm going to just do this calculation.
03:24
And that would be which is.
03:27
So this is 571 ,000.
03:30
Sorry, this is 5771 ,000...