The Normal Distribution
The normal probability distribution should need no introduction. Some of you may already know it as the “bell-shaped curve.” Actually, the normal probability distribution is a family of distributions; the members of the family can differ in mean and standard deviation, but all have their shape in common. That is, they are similar in shape in the same sense that two triangles are similar in geometry, up to a point. As it turns out, it is extremely difficult to determine by visualization whether a distribution is normal or not. Indeed, some normal distributions appear “tall and skinny,” while others appear “wide and flat.” However, as we will highlight, they all share certain characteristics. To illustrate our point, consider some “typical” normal distributions depicted in Figure 10.1. The three distributions have different means and standard deviations, making them appear different. However, these distributions are all normal distributions. Normal distributions are all unimodal and symmetric, sharing in common their basis in the density function for the normal probability distribution, which we will describe soon.