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The normal distribution, or Gaussian distribution, is a symmetrical distribution commonly referred to as the bell curve. It can be considered as a special case of the binomial distribution with a very large number of trials ( ) and an equal success/failure rate ( ).
Suppose that the mean value and standard deviation of a normal distribution are  and  , respectively. The normal distribution has the following important properties. See plots of normal distributions.
| Normal Distribution |
Density Function  |  |
Distribution Function  |  |
| Mean | |
Variance  | |
| Standard Deviation | |
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and zero success rate anywhere else. The uniform distribution has the following important properties. 
and the probability of the desired outcome diminishes as the trial number increases (
). 
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