*43*

The binomial distribution is one of the most commonly used distributions in all of statistics.

On a TI-84 calculator there are two functions you can use to find probabilities related to the binomial distribution:

**binompdf(n, p, x)**: Finds the probability that**exactlyÂ**duringÂ*x*successes occur*n*trials where the probability of success on a given trial is equal toÂ*p*.**binomcdf(n, p, x)**: Finds the probability thatduring*x*successes or fewer occur*n*trials where the probability of success on a given trial is equal toÂ*p*.

You can access each of these functionsÂ on a TI-84 calculator by pressing 2ndÂ and then pressingÂ VARS. This will take you to a **DISTR **screen where you can then use **binompdf()** and **binomcdf()**:

The following examples show how to use each of these functions in practice.

**Examples: How to Use Binompdf()**

The following examples show how to use the **binompdf()** function.

**Example 1: Free-Throw Attempts**

Jessica makes 80% of her free-throw attempts. If she shoots 10 free throws, what is the probability that she makes exactly 7?

To answer this, we can type in the following formula:

The probability that she makes exactly 7 isÂ **.2013**.

**Example 2: Fraudulent Transactions**

A bank knows that 3% of all transactions are fraudulent. If 20 transactions occur in a given day, what is the probability that exactly 2 are fraudulent?

To answer this, we can type in the following formula:

The probability that exactly 2 transactions are fraudulent is **.0988**.

**Examples: How to Use Binomcdf()**

The following examples show how to use the **binomcdf()** function.

**Example 1: Free-Throw Attempts**

Jessica makes 50% of her free-throw attempts. If she shoots 10 free throws, what is the probability that she makes 7 or less?

To answer this, we can type in the following formula:

The probability that she makes 7 or less free throws is **.9453**.

**Example 2: Fraudulent Transactions**

A bank knows that 3% of all transactions are fraudulent. If 20 transactions occur in a given day, what is the probability that more than 2 transactions are fraudulent?

To answer this, we can type in the following formula:

The probability that more than 2 transactions are fraudulent is **.021**.

**Additional Resources**

Binomial Distribution Calculator

How to Perform a Binomial Test in Excel