The normal distribution is pattern for the distribution of a set of data which follows a bell shaped curve. In many natural processes, random variation conforms to a particular probability distribution known as the normal distribution, which is th most commonly observed probability distribution. It is also known as the Gaussian distribution among the scientific community. A normal distribution is described by its mean 
and standard deviation 
. The density curve is symmetrical, centered about its mean, with its spread determined by its standard deviation.
and standard deviation . The density curve is symmetrical, centered about its mean, with its spread determined by its standard deviation. The shape of the curve is described as bell-shaped with the graph falling off evenly on either side of the mean. 50% of the distribution lies to the left of the mean and 50% lies to the right of the mean. The spread of a normal distribution is controlled by the standard deviation
The Standard Normal curve, shown above, has mean value 0 and standard deviation 1. If a dataset follows a normal distribution, then about 68% of the observations will fall within of the mean , which in this case is with the interval (-1,1). About 95% of the observations will fall within 2 standard deviations of the mean, which is the interval (-2,2) for the standard normal, and about 99.7% of the observations will fall within 3 standard deviations of the mean, which corresponds to the interval (-3,3) in this case. Although it may appear as if a normal distribution does not include any values beyond a certain interval, the density is actually positive for all values, 
. Data from any normal distribution may be transformed into data following the standard normal distribution by subtracting the mean and dividing by the standard deviation .
of the mean , which in this case is with the interval (-1,1). About 95% of the observations will fall within 2 standard deviations of the mean, which is the interval (-2,2) for the standard normal, and about 99.7% of the observations will fall within 3 standard deviations of the mean, which corresponds to the interval (-3,3) in this case. Although it may appear as if a normal distribution does not include any values beyond a certain interval, the density is actually positive for all values, . Data from any normal distribution may be transformed into data following the standard normal distribution by subtracting the mean and dividing by the standard deviation .The bell shaped curve has several characteristics:
- The curve concentrated in the center and decreases on either side. This means that the data has less of a tendency to produce unusually extreme values, compared to some other distributions.
- The bell shaped curve is symmetric. This tells you that he probability of deviations from the mean are comparable in either direction.
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