00:01
So we're told that the mean of the high school freshman coming in for that year have a gpa mean of 3 .3 with a standard deviation of 0 .35.
00:12
And it said that it was roughly mound shaped and with only a slight skew.
00:18
So just slight skew.
00:20
And so our central limit theorem tells us that, yeah, we like to have sample sizes greater than are equal to 30.
00:26
But if this is pretty close to a normal distribution, and we take samples of size 25 to be in a particular class, that that sampling distribution would be approximately normal.
00:41
And just because our sample size is not greater than 30, doesn't mean that it won't take on that shape, because this distribution is only slightly skewed and it's quite mound shape.
00:51
So it would have a mean that would center at about 3 .3, and it would have a standard deviation that would center at 0 .35 divided by the square root of 25, which is 0 .35 divided by 5, so 0 .07.
01:10
And our picture would look like approximately this for our sampling distribution, that if we have it centered at 3 .3, and again, this is our sampling distribution of x bars, each coming from a sample size of 25.
01:32
And so if we go out one standard deviation, we go out .07...