00:01
And so the mean is 78 and the variance is 36.
00:04
We want to find the probability that a person taking the exam scores higher than 72.
00:08
So utilizing the z we're going to have 72 minus 78 over 36 or the square root of 36.
00:29
There's going to be a probability of z being greater than it's going to be 6 over 6 which is 1.
00:39
So when the z score is 1 then we'll have a probability to be 0 .841.
00:54
So next we want to suppose that the student scoring in the top 10 percent of this distribution are to receive an a grade.
01:02
So what is the minimum score a student needs to achieve a earn a grade of an a.
01:07
So looking for the z value that corresponds with the top 10 percent.
01:17
So let's find our z value that will correspond to that.
01:27
So that z value is going to be negative 1 .282 which is going to be less than x minus 72 over the square root of 36.
01:41
So our x value here is going to be negative 1 .282 times 6 plus 72.
01:51
So we end up with 64 .308.
02:01
For c it says what must be the cutoff point for passing the examination if the instructor wants only the top 28 percent.
02:09
So same approach we now want the top 28 percent or 28 .1 percent.
02:22
So therefore we're looking for z to be 0 .719.
02:28
So let's find the z value that corresponds to that.
02:34
So that z value is going to be 0 .58.
02:44
So our x value is going to be 0 .58 times 6 plus 72.
02:53
So that gives us 75 .48.
03:02
So i just realized on the previous question we're looking for the top 10 percent.
03:09
So this actually should have been 0 .9 instead of 0 .1.
03:13
So let's redo part b.
03:22
So looking for the z value that corresponds to 0 .9.
03:29
So that's going to be 1 .282...