How to Calculate Normal Probabilities on a TI-84 Calculator

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The normal distribution is 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 normal distribution probabilities:

normalpdf(x, μ, σ) returns the probability associated with the normal pdf where:

• x = individual value
• μ = population mean
• σ = population standard deviation

normalcdf(lower_x, upper_x, μ, σ) returns the cumulative probability associated with the normal cdf between two values.

where:

• lower_x = lower individual value
• upper_x = upper individual value
• μ = population mean
• σ = population standard deviation

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 normalpdf() and normalcdf():

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

Example 1: Normal probability greater than x

Question: For a normal distribution with mean = 40 and standard deviation = 6, find the probability that a value is greater than 45.

Answer: Use the function normalcdf(x, 10000, μ, σ):

normalcdf(45, 10000, 40, 6) = 0.2023

Note: Since the function requires an upper_x value, we just use 10000.

Example 2: Normal probability less than x

Question: For a normal distribution with mean = 100 and standard deviation = 11.3, find the probability that a value is less than 98.

Answer: Use the function normalcdf(-10000, x, μ, σ):

normalcdf(-10000, 98, 100, 11.3) = 0.4298

Note: Since the function requires a lower_x value, we just use -10000.

Example 3: Normal probability between two values

Question: For a normal distribution with mean = 50 and standard deviation = 4, find the probability that a value is between 48 and 52.

Answer: Use the function normalcdf(smaller_x, larger_x, μ, σ)

normalcdf(48, 52, 50, 4) = 0.3829

Example 4: Normal probability outside of two values

Question: For a normal distribution with mean = 22 and standard deviation = 4, find the probability that a value is less than 20 or greater than 24

Answer: Use the function normalcdf(-10000, smaller_x, μ, σ) + normalcdf(larger_x, 10000, μ, σ)

normalcdf(-10000, 20, 22, 4) + normalcdf(24, 10000, 22, 4) = 0.6171