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. Because area under a curve may seem like a strange concept to many introductory statistics students, a short intermission is proposed at this point to introduce the concept.
Area is a familiar concept.
It is valuable to know these formulas if one is purchasing such things as carpeting, shingles, etc. Areas may be added or subtracted from one another to find some resultant area. For example, suppose one had an L-shaped room and wished to purchase new carpet. One could find the area by taking the total area of the larger rectangle and subtracting the area of the rectangle that was not needed, or one could divide the area into two rectangles, find the area of each, and add the areas together. In other cases the areas must be approximated.