The binomial distribution is one of the most commonly used distributions in all of statistics. This tutorial explains how to use the following functions on a TI-84 calculator to find binomial probabilities:

**binompdf(n, p, x) **returns the probability associated with the binomial pdf.

**binomcdf(n, p, x) **returns the cumulative probability associated with the binomial cdf.

where:

**n**= number of trials**p**= probability of success on a given trial**x**= total number of successes

Both of these functions can be accessed 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 illustrate how to use these functions to answer different questions.

**Example 1: Binomial probability of exactly x successes**

**Question: **Nathan makes 60% of his free-throw attempts. If he shoots 12 free throws, what is the probability that he makes exactly 10?

**Answer: **Use the function binomialpdf(n, p, x):

**binomialpdf(12, .60, 10) = 0.0639**

**Example 2: Binomial probability of less than x successes**

**Question: **Nathan makes 60% of his free-throw attempts. If he shoots 12 free throws, what is the probability that he makes less than 10?

**Answer: **Use the function** binomialcdf(n, p, x-1)**:

**binomialcdf(12, .60, 9) = 0.9166**

**Example 3: Binomial probability of at most x successes**

**Question: **Nathan makes 60% of his free-throw attempts. If he shoots 12 free throws, what is the probability that he makes at most 10?

**Answer: **Use the function** binomialcdf(n, p, x)**:

**binomialcdf(12, .60, 10) = 0.9804**

**Example 4: Binomial probability of more than x successes**

**Question: **Nathan makes 60% of his free-throw attempts. If he shoots 12 free throws, what is the probability that he makes more than 10?

**Answer: **Use the function** 1 – binomialcdf(n, p, x)**:

**1 – binomialcdf(12, .60, 10) = 0.0196**

**Example 5: Binomial probability of at least x successes**

**Question: **Nathan makes 60% of his free-throw attempts. If he shoots 12 free throws, what is the probability that he makes more than 10?

**Answer: **Use the function** 1 – binomialcdf(n, p, x-1)**:

**1 – binomialcdf(12, .60, 9) = 0.0834**