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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)Â **returns the probability associated with the binomial pdf.

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

where:

**nÂ**= number of trials**pÂ**= probability of success on a given trial**xÂ**= total number of successes

Both of these functions can be accessed on a TI-84 calculator by pressingÂ 2ndÂ and then pressingÂ vars. This will take you to aÂ **DISTRÂ **screen where you can then useÂ **binompdf()Â **andÂ **binomcdf()**:

The following examples illustrate how to use these functions to answer different questions.

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

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

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

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

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

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

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

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

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

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

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

**Question:Â **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:Â **Use the function**Â 1 â€“ binomialcdf(n, p, x)**:

**1 â€“ binomialcdf(12, .60, 10) = 0.0196**

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

**Question:Â **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:Â **Use the function**Â 1 â€“ binomialcdf(n, p, x-1)**:

**1 â€“ binomialcdf(12, .60, 9) = 0.0834**