00:01
So you have a normal distribution, and this normal distribution is for individual measures, and it has a mean of 70.
00:09
I'm not worried about what the unit is and a standard deviation of 1 .9.
00:13
And so we want to find, if n is 16 and you find an x bar, how likely is it to get the x bar to be somewhere from 69 to 71? and now remember, this distribution is for individuals.
00:30
The distribution that would be for means of 16 items would still be normal since the original is normal.
00:39
But the standard deviation here is going to end up being that 1 .9 divided by the square root of 16, which is divided by 4.
00:48
So the standard deviation will be one -fourth is wide.
00:51
So let's convert these to z values.
00:54
And the z values 69 minus 70 divided by the 1 .9 over the square root of 16 and now it's a z value and then the 71 minus 70.
01:06
So we know that the z values are just opposites.
01:09
So let's quick do that calculation and then find the area between.
01:15
So we have, sorry, i'm just trying my calculator on.
01:18
So that first one is that 1 divided by left parentheses 1 .9 divided by the 6 .9 divided by the square root of 16 or divided by 4.
01:28
And that gives us a, it's going to round two, it's negative 2 .105.
01:36
Now i don't know whether you're using, and this one is positive 2 .105.
01:44
So now, if you're using software to find what this value is, then you can use your normal cdf to plug these values in and negative 2 .1105 and the other upper is 2 .105.
02:03
And then you can find the area between.
02:06
And that will end up being 0 .9647 to four decimal places.
02:12
Now, if you're supposed to use your table and round, i would round this to negative 2 .11...