00:01
Hi, i'm david and i'm here to help you on seeing your question.
00:03
In the question here, we are going to discuss about the central limit theorem.
00:10
And the theorem says that if we have the n greater equal to the 30, the sample mean x -bow will be approximately to the normal, in such a way that if the x -bow will minus the mean of a standard division, divide me square of n, we obtain the standard normal.
00:24
In the question here, we have the n equal to the 86, so it's greater than 30 already.
00:29
The mean equal to the 90, standard division equal to the 24.
00:36
In the first question 1, i'm going to find the probability that the x bar will be less than the 89.
00:45
To find this probability, we need to convert the x1 into the z.
00:49
And by applying the formula here, we will have the 89 we minus the mean over the standard deviation, divide with square root into the n.
00:58
And if you compute it has the z will be smaller than minus 1 ,024 times square, the 86, equal to the minus 0 .3864.
01:11
Now using the calculator we can compute this one, and we get it will be the minus 0 .364...