For example, 0.3413 of the curve falls between the mean and one standard deviation above the mean, which means that about 34 percent of all the values of a normally distributed variable are between the mean and one standard deviation above it. It also means that there is a 0.3413 chance that a value drawn at random from the distribution will lie between these two points.
Sections of the curve above and below the mean may be added together to find the probability of obtaining a value within (plus or minus) a given number of standard deviations of the mean (see Figure 2). For example, the amount of curve area between one standard deviation above the mean and one standard deviation below is 0.3413 + 0.3413 = 0.6826, which means that approximately 68.26 percent of the values lie in that range. Similarly, about 95 percent of the values lie within two standard deviations of the mean, and 99.7 percent of the values lie within three standard deviations.
Figure 2.The normal curve and the area under the curve between σ units.