00:01
So you know you have a normal distribution and there's a certain mean and you know the standard deviation is one and it's one ounce.
00:11
And we know for a sample size of nine that the probability of the difference between a mean of nine and the population mean being within 0 .32 ounces is equal to 0 .6629.
00:27
And that you're not going to use and you want to now change the sample size to 16.
00:35
So this means that the probability of the difference being between the mean and this is 0 .32 and we need to convert it to a z value.
00:50
And that z value, i'll do this one time, is going to end up being that negative 0 .32 divided by that 1 over the square root of 16 and this will be positive point 3 -2 and then one over the square root of 16.
01:06
And so these z values end up being, and that is one -fourth, they come out to be 1 .28 negative and 1 .28 positive.
01:21
And so the area between, and i'm just going to give you the answer for this, the area between negative 1 .28 and 1 .28 for the z values.
01:33
I'm using my normal cdf rather than going through and subtracting the numbers in the table.
01:39
It comes out to be 0 .79945, and you can round that the way you want, or you can look it up in the table and find that answer.
01:46
On part b, you want to change that for sample sizes of 25, 36, 49, and 64.
01:59
And so the only thing that's going to change are these samples right here.
02:06
So on this first one, the z values will be, and the first one will be, that will be a square root of 25, so that will be a 1 -5th.
02:17
And the z values will be negative 1 .6 to 1 .6.
02:24
436.
02:25
Putting 36 here, that's going to be a 1 .6.
02:29
So that's going to be a 1 .92 to 1 .92.
02:40
And i'll find these values in a second.
02:42
And this one will be for 1 -7...