00:01
Said at least 100.
00:02
So 100 or more of these 400 have impurities that are fewer than 10 grams.
00:15
So the first thing we need to do is we need to find what is the probability that an individual bag has less than 10 grams of impurities.
00:26
So 10 grams is going to be about one standard deviation away.
00:30
And we've got to find that first.
00:31
So let's figure out what that z value is.
00:34
And so that z value is 10 minus the 12 .2 divided by the 2 .8.
00:40
And so that is negative 2 .2 divided by 2 .8.
00:46
And that z value comes out to be about negative .79 to two decimal places so i can look it up on my chart.
00:56
And the area below negative 0 .79 is 0 .2148.
01:02
So that is the likelihood that that happens.
01:05
And we want to know in 400 of these bags, what's the likelihood that at least 100 of them have that impurity? so we have now that, quote, binomial setting that is approximately normal because n times p, and our little p up here, well, let's start going in another color.
01:25
Our little p value for being less than 10 grams is going to end up being that .214.
01:32
So it is approximately normal with a mean of n times the p and 0 .2148 and then times 400.
01:49
Whoops, sorry, i'm just typing some stuff in here wrong.
01:56
There we go...