Statistics How To

Probability Distribution: List of Statistical Distributions

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Definition of a Probability Distribution
A to Z List of Distributions

What is a Probability Distribution?

A probability distribution tells you what the probability of an event happening is. Probability distributions can show simple events, like tossing a coin or picking a card. They can also show much more complex events, like the probability of a certain drug successfully treating cancer.

There are many different types of probability distributions in statistics including:

The sum of all the probabilities in a probability distribution is always 100% (or 1 as a decimal).

Ways of Displaying Probability Distributions

Probability distributions can be shown in tables and graphs or they can also be described by a formula. For example, the binomial formula is used to calculate binomial probabilities.

The following table shows the probability distribution of a tomato packing plant receiving rotten tomatoes. Note that if you add all of the probabilities in the second row, they add up to 1 (.95 + .02 +.02 + 0.01 = 1).

probability distribution toms

The following graph shows a standard normal distribution, which is probably the most widely used probability distribution. The standard normal distribution is also known as the “bell curve.” Lots of natural phenomenon fit the bell curve, including heights, weights and IQ scores. The normal curve is a continuous probability distribution, so instead of adding up individual probabilities under the curve we say that the total area under the curve is 1.

In a normal distribution, the percentages of scores you can expect to find for any standard deviations from the mean are the same.

In a normal distribution, the percentages of scores you can expect to find for any standard deviations from the mean are the same.

Note: Finding the area under a curve requires a little integral calculus, which you won’t get into in elementary statistics. Therefore, you’ll have to take a leap of faith and just accept that the area under the curve is 1!


Gonick, L. (1993). The Cartoon Guide to Statistics. HarperPerennial.
Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences, Wiley.

List of Statistical Distributions

Click any of the distributions for more information.

See also:

Stephanie Glen. "Probability Distribution: List of Statistical Distributions" From Elementary Statistics for the rest of us!

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