Standard distribution is an extremely important distribution. It is also known as normal distribution. Standard distribution and its associated probabilities are an integral part of statistical process control. When large enough sample sizes are taken, many statistics are normally distributed regardless of the shape of underlying distribution from which they are drawn. We represent a standard distribution by a normal curve.
Standard distribution exhibits the following characteristics.
· It is continuous.
· It is symmetrical distribution about its mean.
· It is asymptotic to the horizontal axis.
· It is unimodal.
· It is a family of the curve.
· Area under the curve is 1.
· All mean, median and mode lie at the same position.
The standard distribution is symmetrical. Each half of the distribution is a mirror image of the other half. Many normal distribution tables contain probability values for only one side of the distribution because probability values for the other side of the distribution are identical because of symmetry.
In theory, the normal distribution is asymptotic to the horizontal axis. That is, it does not touch the x axis, and it goes forever in each direction. The reality is that most applications of the normal curve are experiments that have finite limits potential outcomes.
For example, even though SAT scores are analyzed by standard distribution, the range of the scores on each part of the SAT is only 200 to 800.
Other example could be the life insurance, height or weight of a person, rent of a house.