When the mean value of a normal distribution is bounded by two standard deviations (plus or minus) then it is expected that

#### 95.5 percent of the values will occur in that wider region.

When the mean value of a normal distribution is bounded by three standard deviations (plus of minus) then it is expected that 99.7 percent of the values will occur in that still wider region. When the distribution's mean is bounded by a plus and a minus standard deviation, the design is considered as *Two-Tailed *because both sides of the distribution are being evaluated. These parameterized regions are crucial to the understanding of Value at Risk (VAR) programs and many option pricing models. Also, many linear analysis techniques depend on the assumption and stability of a normal and independent probability functions. Many option pricing models use the annualized standard deviation as the volatility proxy.