A bell curve is often referred to as the normal distribution, with mean μ and variance σ².  A bell curve is perfectly symmetric about the mean and its spread is measured by the standard deviation σ.  This distribution approximates the probability distributions of numerous random variables.

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For example, variables ranging from the outcomes of flips of a coin or the rolls of dice to the number of grains of sand in a cubic yard to the height, weight, or cholesterol levels of 30-year-old American males to the prices of gasoline in North Carolina to all tend to be normally distributed and describable by a bell curve.

This table identifies the percentage of the events expected to fall around the estimated mean of a variable with a normal probability distribution (a bell curve), within plus or minus the specified numbers of standard deviations.

range

confidence interval

1 σ

68.3%

2 σ

95.4%

3 σ

99.7%

4 σ

99.9%