 The normal distribution is such a big topic that we'll have to do this as a part 2. So we know some values for the area under the normal distribution curve. Within one standard deviation, we have 68% of the area. Within 2, we have 95%. And within 3, we have 99.7%. And if I were a nice and kind math teacher, or the universe were a good and pleasant place, then every problem involving the normal distribution would only require knowing 68, 95, 99.7%. But you know what I'm going to say to that? I am not nice and kind, and neither is the universe. Fortunately, most statistical calculators, spreadsheets, and random bone-apps have a norm-dist function. Now for practical reasons, these compute the area under the normal distribution up to a requested value. And a common syntax looks something like norm-dist, the value you want, the mean of the normal distribution, and the standard deviation of the normal distribution. So let's take a look at another example. Once again, we have our serial boxes, where the weight of serial is normally distributed with a mean of 16 and a standard deviation of 0.2. And this time we're interested in knowing how many of a thousand boxes can be expected to contain more than 15.8 ounces. Since we know the mean and the normal distribution is symmetric about the mean, we can sketch a picture of the normal distribution. Again, the peak of the normal distribution is located at the mean, 16 ounces. We want more than 15.8 ounces. So that's this area, starting at 15.8 ounces, and going to the right. Now, the norm-dist function will generally allow us to calculate the area up to a certain point, which means we can't use it to calculate the area to the right of 15.8, but we can use it to calculate the area up to 15.8. So we'll use our technological tool. And this tells us that the area up to x equals 15.8 is about 0.1587. This means that about 15.87% of the area is to the left of x equals 15.8, so 100 minus 15.87, or about 84.13% of the area, is to the right of x equals 15.8, and the area is the probability, so the probability the weight is greater than 15.8 ounces, is 84.13%. Or let's take another example. Use a random application to find the probability a normally distributed quantity with mean of 70 and standard deviation of 3 is between 72 and 74. So we'll pull out our power tool and calculate. And because we're using a power tool without protection, we very quickly get to the wrong answer. So again, the important thing to understand is that if you use a power tool without understanding how it works, you risk getting the wrong answer very quickly. And that's great if your goal is to get a lot of wrong answers. But assuming that we actually want to get correct answers, it's important that we take the proper precautions. And what this means with the normal distribution is we draw a picture. Since we know the mean, and the normal distribution is symmetric about the mean, we can sketch a picture of the normal distribution. And since the probability corresponds to the area, we can identify the area we need to find. And that area will be this region between 72 and 74. So remember that our randomly chosen application can tell us the area up to a certain point. So our randomly chosen application tells us that the area up to x equals 72 is 74.75%. And if we keep going all the way up to 74, we get an area of 90.88%. And what's important to recognize is that 90.88% is the entire area, the blue and the green pieces together. Well, the probability is the area. So if I just want the green pieces, I'm going to take the entire area, 90.88%, and I'm going to subtract the area I don't want, 74.75%. And when I do that subtraction, I get the probability...