NORM.DIST

Calculates the probability density function (PDF) or the cumulative distribution function (CDF) of a normal distribution.

Syntax:

NORM.DIST(x, mean, standard_dev, cumulative)

x is required, and the value that you want to use to calculate the normal distribution of.

mean is required, and is the mean of the normal distribution.

standard_dev is required, and is the standard deviation of the normal distribution.

cumulative is required, and is a logical value:

TRUE: Returns the cumulative distribution function (the probability that a random variable is less than or equal to x).

FALSE: Returns the probability density function (the height of the normal distribution curve at x).

Example:

If x contains 80, mean contains 75, standard_dev contains 10 and cumulative contains TRUE:

NORM.DIST(80, 75, 10, TRUE)

returns 0.691462461

This example finds the probability of a student scoring less than or equal to 80.

x:

mean:

standard_dev:

Cumulative:

Result:

0.691462461

Application:

Employee Commute Times

A large company wants to analyze the commute times of its employees. They have collected data and found that the commute times are approximately normally distributed.

Average (Mean) commute time (μ): 45 minutes
Standard Deviation (σ): 10 minutes

The company wants to answer the following questions:

What is the probability that a randomly selected employee has a commute time of exactly 50 minutes? (This uses the PDF)
What is the probability that a randomly selected employee has a commute time of 50 minutes or less? (This uses the CDF)

Table of NORM.DIST Function Usage

	Question	NORM.DIST Function Parameters	Description	NORM.DIST Formula	Result
	A	B	C	D	E
1	PDF
2		x: 50 minutes (the value you want to evaluate)	Calculates the probability density at x=50. This is used to find the likelihood of a specific value.
3		mean: 45 minutes	The average of the distribution.
4		standard_dev: 10 minutes	The standard deviation of the distribution.
5		cumulative: FALSE	Specifies that you want the probability density function (PDF), not the cumulative distribution function.
6				NORM.DIST(50, 45, 10, FALSE)	0.0352
7	CDF
8		x: 50 minutes (the upper bound)	Calculates the cumulative probability from negative infinity up to x=50.
9		mean: 45 minutes	The average of the distribution.
10		standard_dev: 10 minutes	The standard deviation of the distribution.
11		cumulative: TRUE	Specifies that you want the cumulative distribution function (CDF), which sums the probabilities up to a given value.
12				NORM.DIST(50, 45, 10, TRUE)	0.6915

Explanation of Results:

PDF Example (Probability of exactly 50 minutes): The result of approximately 0.0352 means that the probability density at exactly 50 minutes is 0.0352. It's important to remember that for a continuous distribution like the normal distribution, the probability of a single exact value is theoretically zero. The PDF value represents the height of the curve at that point, which is an indicator of the relative likelihood.

CDF Example (Probability of 50 minutes or less): The result of approximately 0.6915 means there is a 69.15% chance that a randomly selected employee will have a commute time of 50 minutes or less. This value represents the total area under the normal distribution curve from negative infinity up to 50.