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.

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

where:

mean = mean number of “successes”= 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():

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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.

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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?