Normal distribution

The normal distribution is a probability distribution used in probability theory and statistics. It is also called Gaussian distribution because it was first discovered by Carl Friedrich Gauss. The normal distribution is very important in many fields because many things take this form. A random variable that takes this form is normally distributed, and can be called a normal deviate. The normal distribution is often called the bell curve, because the graph of its probability density looks like a bell. The standard normal distribution (also known as the Z distribution) is a normal distribution that has a mean of zero and a standard deviation of one. 

The form of the distribution is  



In a normal distribution, the parameter  is the mean ("average"). The standard deviation ("variability") is . The variance of the distribution is .

The normal distribution is important because it can represent real-life examples. It is used in natural and social sciences. Some examples include:
Height
Test scores
Measurement errors
Light intensity (as in laser light)
Insurance companies use normal distributions to model certain average cases.
The central limit theorem can be used to describe real-life data as a normal distribution.

 Origin 
Its origin goes back to the 18th century to De Moivre and in the early 19th century with Gauss.

 Use 
It is the most widely used piece of statistics by far. It was famously used in World War I by the United States Army to decide when men were so poor mentally that they could not be used by the Army in any job. 

 Related pages 
 Frequency distribution
 Least squares
 Student's t-distribution

 References 

 Other websites 
Cumulative Area Under the Standard Normal Curve Calculator  from Daniel Soper's Free Statistics Calculators website. Computes the cumulative area under the normal curve (i.e., the cumulative probability), given a z-score.
Interactive Standard Normal Distribution
GNU Scientific Library – Reference Manual – The Gaussian Distribution
Normal Distribution Table
Download free two-way normal distribution calculator
Download free normal distribution fitting software

Category:Probability distributions