# Statistics Dictionary

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### Normal Distribution

The normal distribution is a probability distribution that associates the normal random variable X with a cumulative probability . The normal distribution is defined by the following equation:

Normal equation. The value of the random variable Y is:

Y = [ 1/σ * sqrt(2π) ] * e -(x - μ)2/2σ2

where X is a normal random variable, μ is the mean, σ is the standard deviation, π is approximately 3.14159, and e is approximately 2.71828.

The graph of the normal distribution depends on two factors - the mean and the standard deviation. The mean of the distribution determines the location of the center of the graph, and the standard deviation determines the height of the graph. When the standard deviation is large, the curve is short and wide; when the standard deviation is small, the curve is tall and narrow. All normal distributions look like a symmetric, bell-shaped curve, as shown below.  The curve on the top is shorter and wider than the curve on the bottom, because the curve on the top has a bigger standard deviation.