## Figure 143

Probability Ranges for a Normal Distribution

When returns display a normal distribution, actual outcomes will lie within ± 1 standard deviation of the mean 68.26 percent of the time, within ±2 standard deviations 95.46 percent of the time, and within ±3 standard deviations 99.74 percent of the time.

### Probability Ranges for a Normal Distribution

When returns display a normal distribution, actual outcomes will lie within ± 1 standard deviation of the mean 68.26 percent of the time, within ±2 standard deviations 95.46 percent of the time, and within ±3 standard deviations 99.74 percent of the time.

Mean or expected value

that in Figure 14.2. Probabilities associated with the outcomes in Figure 14.1 are given by the heights of the bars, whereas in Figure 14.2, the probabilities must be found by calculating the area under the curve between points of interest.

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