00:01
Hi, i'm david and i'm here to have you answering your question.
00:03
In this question here, we are going to discuss about the central limit theorem.
00:07
And it says, if we have the n -quited equal to the county, and then the sum of mean x -bile could be approximately to the normal.
00:15
Where we have the mean of the x -bile equal to the mean of the population, standard division x -bile equal to the sigma divan be squared to the n.
00:23
Also, if we think the x -bile will manage the mean over the standard deviation, we obtain the standard normal.
00:29
In this question here we have the symbol size.
00:33
First we have the mean equal to the 22 and the standard division equal to the 17.
00:40
Now in the first question 8, we're given the n equal to the 43, quite than 30 already.
00:47
Therefore we have the first of the x bar by the formula equal to the mean and equal to the 22, sigma under x -par by the formula equal to the sigma divide by square root on the 43 and then get equal to the 17 divided square root and then get equal to the 17 divided square and the 43 get equal to the 2 .59 i will round to the 4 decimal places this one to the 2 decimal places will be the 59 and then the next one needs to find the probability that the x -par it will be between the the 22 to the 24.
01:28
And to find this probability i can do the xx into the z.
01:32
And to do it, i need to apply this formula here.
01:35
And then we get equal to the 22 minus the mean will be, the mean will be the 22 over the standard division 2 .59.
01:45
24 minus 22 over the 2 .59.
01:49
And if we compute it, we have the z will be between...