00:01
So here we're looking for the first and third quartiles of our given distribution, where we know that x is distributed as a normal distribution, with a mean value of 27, and a standard deviation of 5.
00:16
Now, the approach that i'll take here is to first find the first and third quartiles of a standard normal distribution, the z star, such that probability of z less than or equal to z star 0 .25, which i'll note, let's second here, so that's going to be our first quartile, as well as we can find the z star such that the probability of z star being, or z, z, less than z star, 0 .75, will be our third quartile, where one thing that i'll note is because of the symmetry, so from the symmetry of z, we have that q1, the first quartile is going to be equal to the negative of the third quartile.
01:09
So i'm going to bring up a normal distribution table here.
01:14
So we have the cumulative probability to the left for a given z score.
01:17
So what we want to do is look on the table for when we have a value of 0 .75 inside.
01:24
You can see that we go from 0 .7486 at 0 .67 to 0 .7517 at 0 .68...