00:01
A random sample of size 36 is to be selected from a population that has a mean of 50 and a standard deviation of 10.
00:12
Part a, the sample of 36 has a mean value of x bar, which belongs to a sampling distribution.
00:18
Find the shape of this sampling distribution.
00:20
The shape of this distribution is going to be approximately normal.
00:28
And that's because our sample size is larger than 30, so it falls under that central limit theorem.
00:34
Part b, find the mean of this sampling distribution.
00:38
The mean is going to mirror the population mean, so that's going to be 50.
00:44
Part c, find the standard error of the sampling distribution.
00:48
So the standard error is taking the population standard deviation divided by the square root of our sample size.
00:54
And when we do that, we get 1 .67...