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Normal Distribution Formula

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The normal distribution is a type of continuous probability distribution for a real-valued random variable. Check FAQs

P normal = \frac{e^{- \frac{{(x - μ)}^{2}}{2 \cdot σ^{2}}}}{σ \cdot \sqrt{2 \cdot π}}

P_normal - Normal Distribution?x - Specific Outcomes within Trials?μ - Mean of Distribution?σ - Standard Deviation of distribution?π - Archimedes' constant?

Normal Distribution Example

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Here is how the Normal Distribution equation looks like with Values.

Here is how the Normal Distribution equation looks like with Units.

Here is how the Normal Distribution equation looks like.

0.0967 = \frac{e^{- \frac{{(3 - 2)}^{2}}{2 \cdot 4^{2}}}}{4 \cdot \sqrt{2 \cdot 3.1416}}

0.0967 = \frac{e^{- \frac{{(3 - 2)}^{2}}{2 \cdot 4^{2}}}}{4 \cdot \sqrt{2 \cdot 3.1416}}

0.0967 = \frac{e^{- \frac{{(3 - 2)}^{2}}{2 \cdot 4^{2}}}}{4 \cdot \sqrt{2 \cdot 3.1416}}

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Normal Distribution Solution

Follow our step by step solution on how to calculate Normal Distribution?

FIRST Step Consider the formula

P normal = \frac{e^{- \frac{{(x - μ)}^{2}}{2 \cdot σ^{2}}}}{σ \cdot \sqrt{2 \cdot π}}

Next Step Substitute values of Variables

∴

P normal = \frac{e^{- \frac{{(3 - 2)}^{2}}{2 \cdot 4^{2}}}}{4 \cdot \sqrt{2 \cdot π}}

Next Step Substitute values of Constants

∴

P normal = \frac{e^{- \frac{{(3 - 2)}^{2}}{2 \cdot 4^{2}}}}{4 \cdot \sqrt{2 \cdot 3.1416}}

Next Step Prepare to Evaluate

∴

P normal = \frac{e^{- \frac{{(3 - 2)}^{2}}{2 \cdot 4^{2}}}}{4 \cdot \sqrt{2 \cdot 3.1416}}

Next Step Evaluate

∴

P normal = 0.0966670292007123

LAST Step Rounding Answer

∴

P normal = 0.0967

Normal Distribution Formula Elements

Variables

Constants

Functions

Normal Distribution

The normal distribution is a type of continuous probability distribution for a real-valued random variable.

Symbol: P_normal

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Normal Distribution

Specific Outcomes within Trials

Specific Outcomes within Trials are the number of times a certain outcome takes place within a given set of trials.

Symbol: x

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Specific Outcomes within Trials

Mean of Distribution

Mean of Distribution is the long-run arithmetic average value of a random variable having that distribution.

Symbol: μ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mean of Distribution

Standard Deviation of distribution

The Standard Deviation of distribution is a measure of how spread out numbers are.

Symbol: σ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Standard Deviation of distribution

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

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How to Evaluate Normal Distribution?

Normal Distribution evaluator uses Normal Distribution = e^(-(Specific Outcomes within Trials-Mean of Distribution)^2/(2*Standard Deviation of distribution^2))/(Standard Deviation of distribution*sqrt(2*pi)) to evaluate the Normal Distribution, The normal distribution is a type of continuous probability distribution for a real-valued random variable. Normal Distribution is denoted by P_normal symbol.

How to evaluate Normal Distribution using this online evaluator? To use this online evaluator for Normal Distribution, enter Specific Outcomes within Trials (x), Mean of Distribution (μ) & Standard Deviation of distribution (σ) and hit the calculate button.

FAQs on Normal Distribution

What is the formula to find Normal Distribution?

The formula of Normal Distribution is expressed as Normal Distribution = e^(-(Specific Outcomes within Trials-Mean of Distribution)^2/(2*Standard Deviation of distribution^2))/(Standard Deviation of distribution*sqrt(2*pi)). Here is an example- 0.096667 = e^(-(3-2)^2/(2*4^2))/(4*sqrt(2*pi)).

How to calculate Normal Distribution?

With Specific Outcomes within Trials (x), Mean of Distribution (μ) & Standard Deviation of distribution (σ) we can find Normal Distribution using the formula - Normal Distribution = e^(-(Specific Outcomes within Trials-Mean of Distribution)^2/(2*Standard Deviation of distribution^2))/(Standard Deviation of distribution*sqrt(2*pi)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

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Normal Distribution Formula

Normal Distribution Example

Normal Distribution Solution

Normal Distribution Formula Elements

Other formulas in Industrial Parameters category

How to Evaluate Normal Distribution?

FAQs on Normal Distribution

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