00:02
To figure out these two probabilities, we have to apply the central limit theorem, which says if we repeatedly took samples, the distribution would be normal with a center of 9 .43, and the standard deviation of the sampling distribution is going to be the standard deviation for the population, 4 .17, divided by the square root of our sample size, 16, which gives us 1 .04.
00:33
So i'm going to number my bell curve by adding 1 .0425 repeatedly to the right and subtracting to the left.
00:42
And our bell curve will look like this.
00:46
And we first now want to ask, what's the probability of the mean for these households is over 9 .5 pounds.
00:52
So on my bell curve, let me find 9 .5 pounds, which will be right about here, we want to figure out this area to the right.
01:01
So to do that, i'm going to need a z score for 9 .5, which we'll get from doing that minus the center, divided by our standard deviation.
01:15
And that comes out to be a z score of 0 .07.
01:20
So now we'll turn to the standard normal probability table and look up a z score of 0 .07...