A nice fact about the normal curve is, that it is completely determined by the mean and the standard deviation. Once we know the mean and the standard deviation, then we know the whole histogram and we can compute percentages. To do that, we first standardize the data. Standardizing means that we take the data, in this case, the height measurements and we subtract of the mean and divide by the standard deviation. Oftentimes, the resulting standardized data is denoted by z. It's called a standardized value or a z-score. Now keep in mind that z has no units. In this example where we looked at heights, heights come in inches, and the mean and the standard deviation all come in inches, but the z-scores have no units whatsoever, and that's simply because we have inches in the numerator and we have inches in the denominator, and so the inches cancel out. Z tells you how many standard deviations the measurement is above or below average. For example, if z = 2, that means the height is two standard deviations above average. If z is -1.5, then we know that the height is 1.5 standard deviations below average. Once we standardize the data, they have mean 0 and standard deviation equal to 1. This is the whole point of the exercise. We already saw that fathers' heights follow the normal curve with a mean of 68.3 inches and a standard deviation of 1.8 inches. After we standardize, the standardized values follow what's called the standard normal curve which has mean 0 and standard deviation 1. Here's a graph of the standard normal curve. You can plot this graph using the equation y = 1 over square root 2 pi times e to -1/2 x-squared. Don't worry, we are not going to use that formula in this class.