00:01
Hi, i'm david and i'm here here here here here here i'm here going to discuss about the central limit theorem and it says that if the sample size n equals or greater than the 30 and then the symbol mean x -par will be approximately to the normal in such a way that the mean under x -par equal to the mean on the population sigma under x -par equal to the sigma the 1 bsquare to the n and if we take the x -par, we minus the mean over the standard deviation, we obtain the standard normal z.
00:36
And in this question here, we're given the symbol size n equals to the 40 and it's greater than 30 already.
00:44
We have the mean equal to the 3 .0 5 and the sigma equal to the 0 .3.
00:52
From here, we can say that the x -par will be approximately to the normal.
00:56
Well, when the mean of the x -par equal to the mean of the population, sigma of the x -par equals to the 0 .3d b squared in the 40, and then get the 0 .3 db square in the 40, get equal to the 0 .047.
01:16
And from here, the first question 8, as we find the probability that the sum of mean x -par, it will be greater equal to the 3 .1.
01:27
Now to find this probability i need to confirm the x into the z by applying the formula here.
01:33
Then that equal to the probability of the 3 .10 minus the mean will be the 3 .05 over the 0 .074 -74...