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.
Additional Resources
Binomial Distribution Calculator
How to Perform a Binomial Test in Excel
This was very helpful. Thank you.
Thanks for all the examples you gave us to work!
Hi Teyana…You are very welcome! We appreciate your support!
In example #1 you establish that Jessica makes 80% of her free throw attempts. That means that out of 10 free throws she’ll make 8 (8/10 = 0.8, & 0.8 *100 = 80%). But in this example she only has to make 7 out of 10. That should be real easy for her, but why does that mean she only got 0.201326592 * 100 = 20.1326592%. Any chance of an explanation?