00:01
Hi, i'm david and i'm here to have you an answer your question.
00:03
Now let me bring up your question here.
00:06
In the question here we are going to discuss about the central limit theorem.
00:11
Let me remind you that if we have the n greater equal to the 30, and then the symbol mean x -bile will be approximately to the normal.
00:19
In such a way that the mean of the x -par equal to the mean of the population, standard division x -par equal to the sigma of a square root -scolitor -n.
00:30
And if we take the x -bought will minus the mean of a standard deviation, we will get the standard normal.
00:41
Now in the question here we have the x, it will be the age of the student.
00:50
It will follow by the uniform between the 5 and the 11.
00:55
And this will be the answer for the first part one there.
01:00
And from here we need to find the mean and the standard deviation of the 1.
01:05
Of distribution.
01:07
So minimum the uniform equal to 11 plus 5 divided by 2, equal to the 16 divided by 2 and equal to 8.
01:16
Standard division equals 11 minus 5 square divided by 12 under the square root.
01:23
Then we get equal to 11 minus 5 square divided by 12.
01:29
Taking the square root will be equal to the 1 .732.
01:39
And in the question 2, we will have the n equal to the 48, therefore the symbol mean x bar will be approximately to the normal, with the mean it will equal to the mean of the population equal to 8 standard division x bar by the formula it will equal to the sigma of the square root square n and equal to the 1 .732, the 1.
02:06
Equal to the n equal to the 48 and if we compute it we get equal to the 0 .25 and the next question asked me to find the probability that the mean here it will be between the 8 and 8 .4.
02:30
Now to find this probability i need to convert the xx into the z.
02:34
To do it i need to apply this formula here...