00:01
Hi, i'm david and i'm here to help to answer your question.
00:04
Now let me bring up the question here.
00:07
In this question we're going to reveal about the sample mean of the population.
00:13
Let me remind you that if n greater equal to zero and then by the center limit theorem, the x bar symbol mean will follow by the normal when the mean of the x bar equal to the mean of the population, the standard division of the x -par, it will equal to the standard division of the population over the square of n.
00:38
And here, we also know that the x -par minus mean of the x -bar over a standard division of the x -par, it will follow by the standard normal.
00:48
Here we are given the mean and the standard division of the population, we have n equals 36, so it's greater than 30.
00:57
And the question asks you know to find the probability that the x part is more than than 71 .5.
01:04
Now in that you do this probability we need to turn the x -par into the z.
01:11
To do that we apply the formula here so we should get now the 71 .5 we minus the mean 79 .6 .76 divided in by the sigma over the square of n and if we compute it, we have the z will be smaller than.
01:35
We have the 71 .5 minus 79 .6 .76, divided by 22 .49 .43 times 6, equal to the minus 2 .18.
01:53
Now to find this probability, i need to bring up the z table.
01:58
So let me copy the z table for you.
02:04
And let me put the table on the right here.
02:09
Now from the table we have the g score equal to minus 1 point, minus 2 .1 8.
02:16
So the corresponding probability equal to the 0146.
02:23
And that's going to be the answer for the question 4.
02:28
Now for the question 2, we have the same thing but now mean will be mean and standard division will be the same thing and will be equal to 36 but here we have to find the x bar it will be changed the 71 .5 up to the 85 so we do the same thing we need to turn the x bar into the z and to do that we need to turn the 71 .5 minus the mean divided by standard deviation of a square of n we do the same thing with the 85 by the 22 .4943 of the 26.
03:21
The value on the left we found it equal to minus 2 .18.
03:26
And the value on the right, we do the 85 minus 79 .676, divided by 22 .4943, 106, equal to the 1 .4 2.
03:44
Now this probability it can be written now as the total probability 1, minus the 1 on the left, and then minus the 1 on the right.
03:55
But because of the symmetry we can put the smaller than minus 1 .42.
04:00
The reason for that because if we try to draw the graph on the normal for the z, and then we have this one will be the 0, this will be the minus 2 .18, this will be the 1 .42...