00:01
Hey there, welcome to numerate.
00:03
We are asked to find the population standard deviation and the sample mean here.
00:11
So with this, to find the sample mean and standard deviation, what we have is going to be our standard deviation of the sampling distribution.
00:27
So this will be equals to the standard deviation, divided by the square root of our sample size.
00:36
So we're going to find the top 1 % and find our sample mean.
00:42
So what we know here is that we have the initial research on the sleep habits of 30 adults.
00:49
So we take the standard deviation 0 .65 divided by the square root of 30, given us the standard deviation of the sampling distribution equaling around so let's see what we get 0 .12 all right now for the sample mean so for the sample mean we would have to find this by finding the z score first so what we can do is set up as the probability for the top 1 % so this would be is greater than the z score equaling 0 .01.
01:37
Hence, we can use a normal distribution table to find our z score.
01:42
So let's see what we get for the top 1%.
01:47
And this will give us a z score of 2 .326...