How to Calculate Normal Distribution Probabilities in Excel


A normal distribution is the most commonly used distribution in all of statistics.

To calculate probabilities related to the normal distribution in Excel, you can use the NORMDIST function, which uses the following basic syntax:

=NORMDIST(x, mean, standard_dev, cumulative)

where:

  • x: The value of interest in the normal distribution
  • mean: The mean of the normal distribution
  • standard_dev: The standard deviation of the normal distribution
  • cumulative: Whether to calculate cumulative probabilities (this is usually TRUE)

The following examples show how to use this function to calculate probabilities related to the normal distribution.

Example 1: Calculate Probability Less than Some Value

Suppose the scores for an exam are normally distributed with a mean of 90 and a standard deviation of 10.

Find the probability that a randomly selected student receives a score less than 80.

The following screenshot shows how to use the NORMDIST() function in Excel to calculate this probability:

The probability that a randomly selected student receives a score less than 80 is 0.1587.

Example 2: Calculate Probability Greater than Some Value

Suppose the scores for an exam are normally distributed with a mean of 90 and a standard deviation of 10.

Find the probability that a randomly selected student receives a score greater than 80.

To find this probability, we can simply do 1 – NORMDIST() in Excel as follows:

The probability that a randomly selected student receives a score greater than 80 is 0.1587.

Example 3: Calculate Probability Between Two Values

Suppose the scores for an exam are normally distributed with a mean of 90 and a standard deviation of 10.

Find the probability that a randomly selected student receives a score between 87 and 93.

To find this probability, we can subtract the larger value of NORMDIST() from the smaller value of another NORMDIST() in Excel as follows:

The probability that a randomly selected student receives a score between 87 and 93 is 0.2358.

Additional Resources

The following tutorials explain how to perform other tasks related to the normal distribution in Excel:

How to Generate a Normal Distribution in Excel
How to Calculate Z-Scores in Excel
How to Make a Bell Curve in Excel

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