00:01
Hi, i'm david and i'm here to have you on seeing your question.
00:03
Here we have totally four, three questions and then let me do one by one for you.
00:09
All of them, they are about the central limit theorem.
00:14
And it says that if we have the n -quiet equal to the 30, then the same will mean x -bar could be approximately to the normal.
00:22
Where we have the mean of the x -bile equal to the mean of the population, and the standard division of x -bile equal to the sigma divide by square into the n.
00:32
And if we turn the x bar, we minus the mean of a standard deviation, we obtain the standard normal.
00:41
Now in the question 1, we are given then the symbol n equal to the 99, and we are given the mean equal to the 158, and the standard division equal to the 27.
00:55
The question asked what is the mean of the summary distribution on the sign 99? so the question asked you to find the mean of the x bar.
01:05
So by the formula, it just equal to the mean of the population equal to 158.
01:11
And that's will be the answer for the question one.
01:14
Now for the question two, we will have now we have the sample and equal to the 143 and we have the mean equal to the 27 .2 standard division equal to the 51.
01:30
The question is going to find the standard division of the x bar and it's just by the formula equal to the sigma divide by square root to the end.
01:42
Then we have the 51 over the square root of the 143 and we get equal to, i have to i have to round this one to it doesn't say so i route to the four decimal places will be the 4 point to 648.
02:00
Now for the question 3 we will have now we have this iq will be x will follow by the normal when the mean equal to a hundred and the standard division equal to the 15 and we have the sample size and equal to the 25 and once you find the probability that the iq's x it will be between the 100 and 10 have a mean a q's will be greater than 110.
02:44
And to find this probability here, we need to apply this formula to convert the x in addition xxpire into the z...