Exploring the Tails of the Normal Distribution

normal distribution parameters

view selection

full distribution

lower tail

upper tail

expand (→) or compress (←) plotted range by this factor

This Demonstration allows you to estimate the area under the tails of the normal distribution curve. Reading the value of the cumulative distribution function (orange curve) for a specific

value gives the area under the probability distribution function (blue curve) to the left (for the lower tail) or to the right (upper tail) of the

value. The probability distribution function can be adjusted to have values for the mean

and standard deviation

in the ranges (-10, 10) and (0.1, 15), respectively.

Details

In the "full distribution" view, the plotted range is set at

±4σ

. This range can be expanded or compressed by using the bottom slider. In the "lower tail" view, the plotted range is set at (

-6σ

-3σ

) to give a view of the tail beyond the typically viewed

3σ

point. Similarly, for the "upper tail" view, the plotted range is set at (

3σ

6σ

). The ranges in these tail views can also be expanded or compressed to home in on the portions of the curves of interest.

External Links

Distribution Function (Wolfram MathWorld)

Normal Distribution (Wolfram MathWorld)

Probability Density Function (Wolfram MathWorld)

Permanent Citation

Joe O'Hara

"Exploring the Tails of the Normal Distribution"
http://demonstrations.wolfram.com/ExploringTheTailsOfTheNormalDistribution/
Wolfram Demonstrations Project
Published: September 28, 2007