00:01
Hi, i'm david and i'm here to help you answer your question.
00:04
Now let me bring up your question here.
00:06
In this question we want to discuss about the central limit theorem.
00:12
Here if n is large and is larger than 30 and then the x bar can be approximated to the normal with the mean of the x bar equal to the mean of the population, standard division of x bar equal to the standard division of the population on the square of n.
00:31
Here we're given the cdc will be the weight.
00:44
It will have the mean equal to the 168 .15 standard division equal to the 68.
00:53
Now in the question a, it will give the sample equal to the 150 and we want to find expected mean of the sample.
01:03
So once you find the mean of the x bar here, it will equal to the meaning of population and equal to the 168 .5.
01:14
And then we ask you to find the standard division of the simple mean.
01:20
So by formula equal to the sigma over square root of n.
01:24
It will equal to the 68 over square root 150.
01:29
If we do the calculation here, divided by square root 150, equal to the 5 .55.
01:38
Now for the c, we want to find the probability that the same mean below the 160.
01:49
To find this probability, we need to turn the xx into the z.
01:53
To do that, we have to turn the 160, we minus the mean up it, and minus divided by its standard deviation.
02:06
And it will compute, we have the z, it will be smaller than the, than 160 minus 168 .5 divided by standard deviation minus 1 .53.
02:21
Now to find this probability i will bring up the z table.
02:27
I will put the table down here for you.
02:32
Now we have the z score equal to the minus 1 .5.
02:36
So the corresponding probability equal to 0 .063...