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, μ, σ)
where:
- lower = lower value of range
- upper = upper value of range
- μ = population mean
- σ = 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 the NORM.DIST() function, which uses the following syntax:
NORM.DIST(x, σ, μ, cumulative)
where:
- x = individual data value
- μ = population mean
- σ = population standard deviation
- cumulative = FALSE calculate the PDF; TRUE calculates the CDF
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:
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.