This makes the normal curve a general-purpose model, able to describe a large number of naturally occurring phenomena, from test scores to the size of the stars. Similarity of Members of the Family of Normal Curves All the members of the family of normal curves, although different, have a number of properties in common. All members of the family of normal curves share the same bell shape, given the X-axis is scaled properly. Most of the area under the curve falls in the middle. All members of the family of normal curves are bilaterally symmetrical.
Human beings are approximately bilaterally symmetrical, with a right and left side.
All members of the family of normal curves have tails that approach, but never touch, the X-axis. The implication of this property is that no matter how far one travels along the number line, in either the positive or negative direction, there will still be some area under any normal curve. Thus, in order to draw the entire normal curve one must have an infinitely long line. Because most of the area under any normal curve falls within a limited range of the number line, only that part of the line segment is drawn for a particular normal curve. This property, in addition to the property of symmetry, implies that the area in each half of the distribution is .50 or one half.