00:01
A certain dry cereal is packaged in 22 ounce boxes, but the normal distribution that determines how they are filled, is a normal distribution, has a mean, mu, of 22 .5 ounces, and a standard deviation, sigma, of 0 .5 ounces.
00:20
So what is the probability of a box being less than 22? so here's our cutoff, 22.
00:27
We want to know everything less than.
00:29
So that's this area here.
00:32
This area is also the proportion that are underweight.
00:36
So if you pick a random box, the probability it will fall into this group is whatever this area is.
00:43
So as we find an area on a normal distribution.
00:45
Well, we don't use raw data, we turn it into a z score.
00:50
And z is equal to x minus mu over sigma.
00:55
So here, z is 22 minus 22 .5, divide by 0 .5, which is minus 1.
01:01
This is saying that this value, 22, is one standard deviation below the mean.
01:09
Now we can take this and find a probability.
01:11
And for this you need either a z score table, a graphical calculator, or something like excel...