NORMDIST

Calculates values for a normal distribution.

Syntax:

NORMDIST(x, μ, σ, mode)

The normal distribution is an often encountered family of continuous probability distributions, with parameters μ (mean) and σ (standard deviation).

If mode is 0, NORMDIST calculates the probability density function of the normal distribution:

$\frac{e ^{- \frac{1}{2} (\frac{x - μ}{σ})^{2}}}{2 πσ}$

If mode is 1, NORMDIST calculates the cumulative distribution function of the normal distribution:

$\int_{- \infty}^{x} \frac{e ^{- \frac{1}{2} (\frac{t - μ}{σ})^{2}}}{2 πσ} d t$

Example:

NORMDIST(70; 63; 5; 0)

returns approximately 0.03.

NORMDIST(70; 63; 5; 1)

returns approximately 0.92.

Application:

The NORMDIST function is useful for calculating the cumulative probability of a given value in a normal distribution. Let's imagine a company that tracks the number of tasks completed by its employees each week. They have found that the number of tasks completed follows a normal distribution.

Scenario:

A company, "InnovateTech Solutions," has a large team of software developers. The number of code tasks completed by their developers per week is normally distributed with a mean (μ) of 50 tasks and a standard deviation (σ) of 10 tasks.

The company's management wants to understand the distribution of developer productivity. They want to answer questions like:

What percentage of developers complete 45 or fewer tasks per week?
What is the likelihood of a developer completing exactly 60 tasks in a week?
What is the probability that a randomly selected developer completes between 40 and 60 tasks?

Using NORMDIST:

The NORMDIST function can be to answer these questions. The syntax for NORMDIST is:

NORMDIST(x, mean, standard_dev, cumulative)

x: The value for which you want to find the distribution.
mean: The arithmetic mean of the distribution.
standard_dev: The standard deviation of the distribution.
cumulative: A logical value (TRUE or FALSE).
- TRUE: Returns the cumulative distribution function (CDF), which is the probability that the value is less than or equal to x. This is the most common use case for real-world problems.
- FALSE: Returns the probability density function (PDF), which is the probability of a specific value.

Example Calculations in a Spreadsheet:

Let's set up a table to demonstrate how to use NORMDIST to answer the management's questions.

	Description	Value	Formula	Result	Interpretation
	A	B	C	D	E
1	Mean Tasks (μ)	50
2	Standard Deviation (σ)	10
3	Question 1: What percentage of developers complete 45 or fewer tasks?	45	NORMDIST(B3, B1, B2, TRUE)	0.3085	Approximately 30.85% of developers complete 45 or fewer tasks.
4	Question 2: What is the likelihood of a developer completing exactly 60 tasks?	60	NORMDIST(B4, B1, B2, FALSE)	0.0242	The probability of a developer completing exactly 60 tasks is very low (approx. 2.42%), as the PDF gives the probability for a single point.
5	Question 3: What is the probability of completing between 40 and 60 tasks?	40	NORMDIST(B5, B1, B2, TRUE)	0.1587	This is the probability of completing 40 or fewer tasks.
6		60	NORMDIST(B6, B1, B2, TRUE)	0.8413	This is the probability of completing 60 or fewer tasks.
7	Final Calculation (Q3)	Probability	D6 - D5	0.6826	The probability of completing between 40 and 60 tasks is approximately 68.26%. This is expected, as this range represents one standard deviation on either side of the mean.