00:01
So we have the mean being 3 .99 inches and with a pretty big standard deviation, 2 .11.
00:08
In the individual's distribution, we don't know the shape.
00:11
However, we are taking a sample of size 60 and then finding an x bar.
00:17
And that sampling distribution will be approximately normal because of the central limit theorem.
00:27
And it will have a mean of x bars that will still be 3 .4.
00:31
However, that standard deviation of x bars will be that 2 .11 divided by the square root of 60.
00:41
So on the first question, we want to find what's the likelihood that the mean is greater than 4 .07.
00:51
And so the mean being greater than 4 .07 is to have a z value that is greater than 4 .07 minus that 3 .07 minus that 3 .9.
01:02
Divided by that standard air for that sampling distribution.
01:08
And that z value comes out to be, make that down just a little bit, that z value comes out to be 0 .29 -2937.
01:22
And so depending on whether you're using your table or if you're using your table or if you're using software, this comes out to be with like normal cdf, comes out to be this value using that entire value.
01:35
If you're just using the .29, just using this .29, the .29 would have an area of .38, read that 5 -9...