Normal Distribution

The relation among risk, standard deviation, and the coefficient of variation can be clarified by examining the characteristics of a normal distribution, as shown in Figure 14.3. A normal distribution has a symmetrical dispersion about the mean or expected value. If a probability distribution is normal, the actual outcome will lie within ± 1 standard deviation of the mean roughly 68 percent of the time; the probability that the actual outcome will be within ± 2 standard deviations of the expected outcome is approximately 95 percent; and there is a greater than 99 percent probability that the actual outcome will occur within ± 3 standard deviations of the mean. The smaller the standard deviation, the tighter the distribution about the expected value and the smaller the probability of an outcome that is very different from the expected value.

Probability distributions can be viewed as a series of discrete values represented by a bar chart, such as in Figure 14.1, or as a continuous function represented by a smooth curve, such as

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