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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, 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**