  # Probability Distribution: List of Statistical 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). 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.

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!