It turns out that if the data follow the normal curve, then there's a rule of thumb which comes in handy in many situations. About two-thirds of the data fall within one standard deviation of the mean. This is called the empirical rule. There's a second part to the empirical rule which says that about 95% of the data fall within two standard deviations of the mean. And in fact, about all of the data fall within three standard deviations of the mean. Let's look at an example. We saw that the height measurements of the fathers have a mean of 68.3 inches and a standard deviation of 1.8 inches. Now, the second part of the empirical rule says that 95% of the data fall within two standard deviations of the mean. That means, if I go two standard deviations below the mean, that is, I take the mean minus two standard deviations, and I go two standard deviations above the mean, then I can tell that 95% of the height measurements fall between 64.7 inches and 71.9 inches. Let's see how the empirical rule looks like when we draw a histogram. Recall that in a histogram, percentages are given by areas. So, if I draw a histogram that looks bell-shaped, then the mean is right in the middle. And if I go one standard deviation above the mean and one standard deviation below the mean, then the empirical rule says that 68% of the data fall between these two numbers. Now, can I say something about how many data are bigger than one standard deviation above the mean? Well, I know if 68% fall in the middle, that leaves 32% on the outside. And since the histogram is symmetric, it must be half on each side. So this would be roughly 16%. Now, let's look at the second part of the empirical rule. The second part talks about going two standard deviations in each direction. So, here's my mean, here's the mean plus two standard deviations, and here's the mean minus two standard deviations. And then I know that 95% of the data fall between these two numbers. So that leaves me 5% outside, and in particular, I get 2.5% on each side.