The Binomial and the Poisson distribution are the most useful theoretical distribution for discrete variables. They relate to the occurrence of distinct events. In order to have mathematical distribution suitable for dealing with quantities whose magnitude is continuously varying, a continuous distribution is needed. The normal distribution is also called the normal probability distribution, is the most useful theoretical distribution for continuous variables.
Many statistical data concerning business and economic problems are displayed in the form of normal distribution.
Like the Poisson distribution, the normal distribution is also regarded as a limiting case of binomial distribution. When n is large and neither p nor q is close to zero the Binomial distribution is approximated by the normal distribution in spite of the fact that the former is a discrete distribution, where as the later is a continuous distribution.
Examples include measurement errors in scientific experiments, anthropometric measurements of fossils, reaction times in psychological experiment, measurements of intelligence and aptitude, scores on various tests and numerous economic measures and indication.
A continuous random variable X is said to follow a normal distribution with parameter µ and σ (or µ and σ2) if the probability function is
Mean = µ
Variance = σ2
Standard deviation = σ