00:01
In your question, you're talking about the weights of oreos in a package, and you're told that they're normally distributed.
00:07
So what i like to do is draw out a normal distribution to illustrate the question.
00:16
Normal distribution is like shown.
00:18
We sometimes call that a bell -shaped curve, where the mean would be at the center.
00:24
And they tell us that's 518.
00:28
Now what we like to do is count out by standard deviations.
00:32
So i'll count up by 4, that's 522, 526, 530.
00:42
Subtracting 4 from the mean takes me 514, 510, and then 506.
00:52
Your question is to find the percentage of packages that will weigh less than 510 grams.
00:59
So that would be this region here.
01:01
So as you notice, it lands on an exact standard deviation.
01:07
I'm going to show you this question two ways.
01:11
Typically with stuff like this where we land on exact standard deviations, you're using what's called the empirical rule for probability, or the 68, 95, 99 .7 rule is another name for it.
01:28
Now what that rule states is that if we go out one standard deviation, we would find 68 % of the data.
01:37
If we go out two standard deviations, we find 95 % of the data.
01:44
And if i went out three standard deviations, which i'm not going to draw because it's going to interfere with our question, we would find 99 .7%.
01:53
So you may be being asked to do this question using this rule, and if that's the case, what we do is take 100%, subtract the 95 % that's between the two standard deviations.
02:12
That 5 % that's left over is split evenly between the upper tail and the lower tail...