*16*

The binomial distribution is used to describe the probability of obtaining *k* successes in *n* binomial experiments.

A binomial experiment is an experiment that has the following properties:

- The experiment consists of n repeated trials.
- Each trial has only two possible outcomes.
- The probability of success, denoted p, is the same for each trial.
- Each trial is independent.

If a random variable *X* follows a binomial distribution, then the probability that *X* = *k* successes can be found by the following formula:

**P(X=k) = _{n}C_{k} * p^{k} * (1-p)^{n-k}**

where:

**n**: number of trials**k**: number of successes**p**: probability of success on a given trial: the number of ways to obtain k successes in n trials_{n}C_{k}

The following example explains how to create a binomial distribution graph in Excel.

**Example: Binomial Distribution Graph in Excel**

To create a binomial distribution graph, we need to first decide on a value for *n* (number of trials) and *p* (probability of success in a given trial):

Next, we need to create a column for each possible number of successes:

Next, we can use the **BINOM.DIST()** function to calculate the binomial probability for the first number of successes:

We can then copy and paste this formula to the remaining cells in column B:

Lastly, we can highlight each of the binomial probabilities, then click the **Insert** tab along the top ribbon, then click the **Insert Column or Bar Chart** icon in the **Charts** group:

The x-axis of the graph shows the number of successes in 8 trials and the y-axis shows the corresponding probability of that many successes.

Note that if you change the value for either *n* or *p*, the graph will automatically change to reflect the new probabilities.

**Additional Resources**

An Introduction to the Binomial Distribution

Understanding the Shape of a Binomial Distribution

5 Real-Life Examples of the Binomial Distribution