00:05
All right.
00:06
So for question a, we're told that the mean is 70 with a standard deviation 20.
00:13
And if we take samples of size 25, then the average distance from the mean from those samples.
00:19
So average distance from the mean is known as our standard deviation.
00:22
So we would do 20 divided by the square root of 25, which is going to be four.
00:28
Okay.
00:28
So if we take samples of size 25, the average distance from the mean would be four.
00:33
If we take samples of size 36, then the average distance from the mean will be 20 divided by the square root of 36, which is going to be 3 .3333.
00:47
Then we've got a new scenario here where our mean is 100, standard deviation is 20.
00:53
We would know if we take a sample size 25, the probability that the sample mean is greater than 85.
01:02
So if we think about that, so our mean is 100.
01:07
Now again, remember, since we're taking a sample size 25, we need to take our standard deviation and divided by the square way to 25.
01:14
So this is going to give us a standard deviation of the sample means of 4.
01:20
So 85 is going to be to the left of 100.
01:26
We're finding all this area in here.
01:30
And if we calculate the z score for 85, so 85 minus 100 divided by 4, we get to the number...