The Poisson 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 Poisson probabilities:

**poissonpdf(mean, x) **returns the probability associated with the Poisson pdf.

**poissoncdf(mean, x) **returns the cumulative probability associated with the Poisson cdf.

where:

**mean**= mean number of “successes”**x**= specific 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 **poissonpdf() **and **poissoncdf()**:

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

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

**Question: **A hardware store sells 3 hammers per day on average. What is the probability that they will sell 5 hammers on a given day?

**Answer: **Use the function poissonpdf(mean, x):

**poissonpdf(3, 5) = 0.1008**

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

**Question: **A hardware store sells 3 hammers per day on average. What is the probability that they will sell less than 5 hammers on a given day?

**Answer: **Use the function poissoncdf(mean, x-1):

**poissoncdf(3, 4) = 0.8153**

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

**Question: **A hardware store sells 3 hammers per day on average. What is the probability that they will sell at most 5 hammers on a given day?

**Answer: **Use the function poissoncdf(mean, x):

**poissoncdf(3, 5) = 0.9161**

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

**Question: **A hardware store sells 3 hammers per day on average. What is the probability that they will sell more than 5 hammers on a given day?

**Answer: **Use the function 1 – poissoncdf(mean, x):

**1 – poissoncdf(3, 5) = 0.0839**

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

**Question: **A hardware store sells 3 hammers per day on average. What is the probability that they will sell at least 5 hammers on a given day?

**Answer: **Use the function 1 – poissoncdf(mean, x-1):

**1 – poissoncdf(3, 4) = 0.1847**