*32*

The NormalCDF function on a TI-83 or TI-84 calculator can be used to find the probability that a normally distributed random variable takes on a value in a certain range.

On a TI-83 or TI-84 calculator, this function uses the following syntax

**normalcdf(lower, upper, Î¼, Ïƒ)**

where:

**lower**= lower value of range**upper**= upper value of range**Î¼Â**= population mean**ÏƒÂ**= population standard deviation

For example, suppose a random variable is normally distributed with a mean of 50 and a standard deviation of 4. The probability that a random variable takes on a value between 48 and 52 can be calculated as:

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

We can replicate this answer in Excel by using theÂ **NORM.DIST()** function, which uses the following syntax:

**NORM.DIST(x,Â Ïƒ, Î¼, cumulative)**

where:

**x**= individual data value**Î¼Â**= population mean**ÏƒÂ**= population standard deviation**cumulative =Â**FALSE calculateÂ the PDF; TRUE calculates the CDFÂ

The following examples show how to use this function in practice.

**Example 1: Probability Between Two Values**

Suppose a random variable is normally distributed with a mean of 50 and a standard deviation of 4. The probability that a random variable takes on a value **between** 48 and 52 can be calculated as:

=NORM.DIST(52, 50, 4, TRUE) - NORM.DIST(48, 50, 4, TRUE)

The following image shows how to perform this calculation in Excel:

The probability turns out to be **0.3829.**

**Example 2: Probability Less Than One Value**

Suppose a random variable is normally distributed with a mean of 50 and a standard deviation of 4. The probability that a random variable takes on a value **less than** 48 can be calculated as:

=NORM.DIST(48, 50, 4, TRUE)

The following image shows how to perform this calculation in Excel:

Â

The probability turns out to be **0.3085.**

**Example 3: Probability Greater Than One Value**

Suppose a random variable is normally distributed with a mean of 50 and a standard deviation of 4. The probability that a random variable takes on a value **greater than** 55 can be calculated as:

=1 - NORM.DIST(55, 50, 4, TRUE)

The following image shows how to perform this calculation in Excel:

The probability turns out to be **0.1056.**

**Additional Resources**

You can also use this Normal CDF Calculator to automatically find probabilities associated with a normal distribution.