# Normal distribution

• Is one of the most popular and well documented probability distributions. It is frequently depicted as the bell-shaped curve. This process underlies much of financial theory and practice. It is often relied upon for modeling efforts because two variables define its location and shape. These two variables are the mean and the standard deviation. It should be noted that normal distributions with larger standard deviations (or variances) are wider or flatter. This is because the greater volatility is dispersed over a wider range. Conversely, smaller standard deviations generate tighter formations which have a pronounced peak appearance. When the mean value of a normal distribution is bounded by one standard deviation (plus or minus) then it is expected that

#### 68.3 percent of the values will occur in that region.

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.

Embedded terms in definition
Distributions
Distribution
Its
Mean
Modeling
Option
Peak
Plus
Probability distribution
Probability function
Probability
Proxy
Range
Risk
Standard deviation
Value at risk
Volatility
Will

Related Terms

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