Normal Distribution Calculator

✖Specific Outcomes within Trials are the number of times a certain outcome takes place within a given set of trials.ⓘ Specific Outcomes within Trials [x]			+10% -10%
✖Mean of Distribution is the long-run arithmetic average value of a random variable having that distribution.ⓘ Mean of Distribution [μ]			+10% -10%
✖The Standard Deviation of distribution is a measure of how spread out numbers are.ⓘ Standard Deviation of distribution [σ]			+10% -10%

✖The normal distribution is a type of continuous probability distribution for a real-valued random variable.ⓘ Normal Distribution [P_normal]

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Normal Distribution Solution

STEP 0: Pre-Calculation Summary

Formula Used

Normal Distribution = e^(-(Specific Outcomes within Trials-Mean of Distribution)^2/(2*Standard Deviation of distribution^2))/(Standard Deviation of distribution*sqrt(2*pi))
P_normal = e^(-(x-μ)^2/(2*σ^2))/(σ*sqrt(2*pi))
This formula uses 2 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249

Functions Used

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., sqrt(Number)

Variables Used

Normal Distribution - The normal distribution is a type of continuous probability distribution for a real-valued random variable.
Specific Outcomes within Trials - Specific Outcomes within Trials are the number of times a certain outcome takes place within a given set of trials.
Mean of Distribution - Mean of Distribution is the long-run arithmetic average value of a random variable having that distribution.
Standard Deviation of distribution - The Standard Deviation of distribution is a measure of how spread out numbers are.

STEP 1: Convert Input(s) to Base Unit

Specific Outcomes within Trials: 3 --> No Conversion Required
Mean of Distribution: 2 --> No Conversion Required
Standard Deviation of distribution: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_normal = e^(-(x-μ)^2/(2*σ^2))/(σ*sqrt(2*pi)) --> e^(-(3-2)^2/(2*4^2))/(4*sqrt(2*pi))

Evaluating ... ...

P_normal = 0.0966670292007123

STEP 3: Convert Result to Output's Unit

0.0966670292007123 --> No Conversion Required

FINAL ANSWER

0.0966670292007123 ≈ 0.096667 <-- Normal Distribution

(Calculation completed in 00.004 seconds)

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Created by Suman Ray Pramanik

Indian Institute of Technology (IIT), Kanpur

Suman Ray Pramanik has created this Calculator and 50+ more calculators!

Verified by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

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Normal Distribution Formula

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What is Normal distribution?

The normal distribution is a type of continuous probability distribution for a real-valued random variable. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution converges to a normal distribution as the number of samples increases.

How to Calculate Normal Distribution?

Normal Distribution calculator 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 calculate 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 calculate Normal Distribution using this online calculator? To use this online calculator for Normal Distribution, enter Specific Outcomes within Trials (x), Mean of Distribution (μ) & Standard Deviation of distribution (σ) and hit the calculate button. Here is how the Normal Distribution calculation can be explained with given input values -> 0.096667 = e^(-(3-2)^2/(2*4^2))/(4*sqrt(2*pi)).

FAQ

What is Normal Distribution?

The normal distribution is a type of continuous probability distribution for a real-valued random variable and is represented as P_normal = e^(-(x-μ)^2/(2*σ^2))/(σ*sqrt(2*pi)) or Normal Distribution = e^(-(Specific Outcomes within Trials-Mean of Distribution)^2/(2*Standard Deviation of distribution^2))/(Standard Deviation of distribution*sqrt(2*pi)). Specific Outcomes within Trials are the number of times a certain outcome takes place within a given set of trials, Mean of Distribution is the long-run arithmetic average value of a random variable having that distribution & The Standard Deviation of distribution is a measure of how spread out numbers are.

How to calculate Normal Distribution?

The normal distribution is a type of continuous probability distribution for a real-valued random variable is calculated using 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 calculate Normal Distribution, you need Specific Outcomes within Trials (x), Mean of Distribution (μ) & Standard Deviation of distribution (σ). With our tool, you need to enter the respective value for Specific Outcomes within Trials, Mean of Distribution & Standard Deviation of distribution and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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