00:02
Our main goal in this problem is to figure out the probability, the mean birth weight of a simple random sample of three children is less than 5 .5 pounds.
00:11
So to do that, we're going to be applying the central limit theorem, and it is okay to use the normal calculations for this problem because the population is normal or is normally distributed.
00:29
And then the central limit theorem says that if we repeatedly took samples of three, the shape, of our sampling distribution is going to be normal, centered at the population average, which is 7 .5, and then the standard deviation of all of our little samples of three is going to be the population standard deviation, 1 .25, divided by the square root of our sample size, which was 3.
01:02
So 1 .25 divided by the square root of 3 makes 0 .72.
01:10
And now i'm in a number my bell curve here by 0 .72 to the left and to the right.
01:19
Those should be equal spacings there.
01:21
We'll pretend.
01:23
So there's my number line all set with a standard deviation of 0 .72 added and subtracted from the mean to the left and to the right.
01:32
And now we want to find where 5 .5 falls on this number line...