00:01
Hi, i'm david and i'm here to help you answer your question.
00:03
Now let me bring up your question here.
00:06
In this question we are given the discrete uniform distribution.
00:11
It is the discrete because we have x only has three values, one, two and three.
00:18
In re tells us that the probability on the x equal to 1, equal to the probability xx2, equal to the probability xx2, and equal to 1 third.
00:31
Now we have the sample n equal to the 36, is selected from this population, find the probability that the symbol mean is greater than 2 .1, but less than 2 .4.
00:43
Now when we talk about the sample mean, if we have n created equal to the 30, then the sample mean x -par will be approximately to the normal with the mean equal to the mean of the x and the standard division of the x bar it will equal to the standard division of the x over the square root of the n now it means that from this distribution we need to be able to find the e of the x now which is equal to the mu so the mean here if we do it we should get the one out of three times one and then plus one out of three times two plus one out of three times three and if we do it we get equal to the one plus two plus three will be six over three equal to two and then we want to find the very standard division that's why we need to find the ex square to find the x square we should get the 1 out of 3 times 1 square plus 1 of 3 times 2 square thus 1 of 3 times 3 square and we get equal to the 1 plus 4 plus 9 will be 14 out of 3 therefore the variance of the x equal to e x square minus e of x square so get equal to the 14 out of 3 minus the 4.
02:27
So get equal to the 2 out of 3.
02:30
And therefore the standard division of the x just equal to the square root 2 out of 3.
02:37
Now it will get the x part in this case, it will follow by the standard normal or the normal with the mean of the x bar equal to 2.
02:48
Standard division on the x bar equal to the square 2 out of 3 over square root of the n, we square root of the 36...