Home Â» How to Calculate Normal Probabilities on a TI-84 Calculator

# How to Calculate Normal Probabilities on a TI-84 Calculator

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, Î¼, Ïƒ)Â returns the probability associated with the normal pdf where:

• xÂ = individual value
• Î¼ = population mean
• Ïƒ = population standard deviation

normalcdf(lower_x, upper_x, Î¼, Ïƒ)Â returns the cumulative probability associated with the normal cdf between two values.

where:

• lower_xÂ = lower individual value
• upper_xÂ = upper individual value
• Î¼ = population mean
• Ïƒ = population standard deviation

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 use normalpdf()Â and normalcdf():

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

### Example 1: Normal probability greater than x

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

Answer:Â Use the function normalcdf(x, 10000, Î¼, Ïƒ):

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

Answer:Â Use the function normalcdf(-10000, x, Î¼, Ïƒ):

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

Answer:Â Use the function normalcdf(smaller_x, larger_x, Î¼, Ïƒ)

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

### Example 4: Normal probability outside of two values

Question:Â 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:Â Use the function normalcdf(-10000, smaller_x, Î¼, Ïƒ) +Â normalcdf(larger_x, 10000, Î¼, Ïƒ)

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