A far more important result than those mentioned above is also related to the fact that the area under the curve is equal to 100 percent. For practical purposes, however, most of the data values (99.73 percent) occur within 3σ of the mean. The area under the curve within these two limits must therefore be equal to unity (i.e., 1.000 or 100 percent). Since it extends indefinitely in either direction (minus infinity to plus infinity), it encompasses all of the results that can occur. The theoretical normal distribution extends out infinitely in both directions and never quite reaches the horizontal axis and has a total area under the curve of 1.00 (i.e., 100 percent of the data values are represented by the distribution).
Such a distribution is very convenient to use because it is characterized by the mean (μ or x) and standard deviation (σ or s).Īs Figure 1 shows, most of the strength measurements cluster around the mean (x = 4,824 psi), while fewer measurements are near the lowest (3,875 psi) and highest (5,975 psi) strength values. Figure 1 illustrates a bell curve, superimposed over a histogram of PCC compressive strength data. Basically, a normal distribution is a bell shaped curve. The normal distribution is a data distribution that can be used to describe many types of measurements in engineering.
