1365X: The Normal Distribution - Shape - Skewed Normal Distribution

The normal curve was developed in 1733 by DeMoivre as an approximation to the binomial distribution. His paper was not discovered until 1924 by Karl Pearson. Laplace used the normal curve in 1783 to describe the distribution of errors. Subsequently, Gauss used the normal curve to analyze astronomical data in 1809. The normal curve is often called the Gaussian distribution. The term bell-shaped curve is often used in everyday usage.

The shape of the normal distribution is determined by two parameters, the mean $\color{blue}{ \mu }$ and the variance $\color{blue}{ { \sigma ^ 2 } }$, and a Normally distributed random variable $\color{blue}{ X }$ is commonly denoted $\color{blue}{ X \sim N(\mu , { \sigma ^ 2 } ) }$.

In the display below you can see the effects of changing the mean and the standard deviation (the square root of the variance).
After selecting "Show Probability", you can also slide the two gliders on the x-axis to see the probability that $\color{blue}{ X }$ falls between them.
Show Probability Show CDF, F(x)