# Normal Random Variable

Measurements collected to represents height, weight and temperature fall under the classification of Continuous Random Variables. Many such continuous variables have bell shaped distributions and are know as Normal Random variables. Theoretically the distribution of a normal random variable is continuous, bell shaped and symmetric about the mean with median and mean coinciding with mean.

The equation for a normal curve is y = $\frac{1}{\sigma \sqrt{2\pi }}e^{\frac{-(x-\mu )^{2}}{2\sigma ^{2}}}$.where μ and σ represent the mean and standard deviation of the random variable which describe a normal distribution completely. The notation used to denote a normal distribution is N(μ, σ^{2}) where σ is the variance of the distribution.

The probabilities of normal random variables are proportional to the area under the normal curve between the two end points that limit the variable. The theoretical normal curve can also be used to study random variable which are only approximately normal.