# BinomPDF vs BinomCDF: The Difference (Plus Examples)

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 exactly x successes occur during n trials where the probability of success on a given trial is equal to p.
• binomcdf(n, p, x): Finds the probability that x successes or fewer occur during n trials where the probability of success on a given trial is equal to p.

You can access each of these functions on a TI-84 calculator by pressing 2nd and then pressing 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 is .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.