Normal distribution is a continuous probability distribution defined by two parameters μ, the mean of the distribution and σ2 the variance. In real world situations distributions of many measures like height of adults, SAT scores, physical conditions like Blood pressure are approximately normal. A normal variable can assume any sub intervals in the interval (-∞, ∞). Normal distribution is also known as Gaussian distribution named after the German mathematician Karl Gauss who published a work describing it.Normal distribution is considered as the most important probability distribution in statistics.

Normal distribution is a symmetric bell shaped distribution of a continuous random variable. It can be considered as the limiting distribution of the binomial random variable. If we analyze the Histograms of a binomial distribution, it can be seen the histogram approaches the normal shape as the parameter n ( number of trials ) increases.
The normal distribution is defined by the mathematical equation,
y = $\frac{e^{\frac{-(X-\mu )^{2}}{2\sigma ^{2}}}}{\sigma \sqrt{2\pi }}$
where μ is the mean and σ is the standard deviation of the distribution.
The value of the mean μ determines the position of the center of the graph for a specific normal variable, while the value of the variance (σ2) determines spread and the peak of the graph as seen below.

Normal Distribution

Normal Distribution Definition