Normal Probability Distribution Calculator

✖Standard Deviation of Normal Distribution is the average distance between each data point and the mean of the distribution, providing a measure of how much the values typically deviate from the mean.ⓘ Standard Deviation of Normal Distribution [σ_Normal]			+10% -10%
✖Number of Successes is the random variable that denotes the number of events or occurrences within a fixed interval of time or space.ⓘ Number of Successes [x]			+10% -10%
✖Mean of Normal Distribution is the average or expected value, and represents the central tendency of the distribution.ⓘ Mean of Normal Distribution [μ_Normal]			+10% -10%

✖Normal Probability Distribution Function also known as the Gaussian distribution, is a mathematical function that describes a symmetrical bell-shaped curve.ⓘ Normal Probability Distribution [P_Normal]

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Formula

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Normal Probability Distribution

Formula

`"P"_{"Normal"} = 1/("σ"_{"Normal"}*sqrt(2*pi))*e^((-1/2)*(("x"-"μ"_{"Normal"})/"σ"_{"Normal"})^2)`

Example

`"0.150569"=1/("2"*sqrt(2*pi))*e^((-1/2)*(("7"-"5.5")/"2")^2)`

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Normal Probability Distribution Solution

STEP 0: Pre-Calculation Summary

Formula Used

Normal Probability Distribution Function = 1/(Standard Deviation of Normal Distribution*sqrt(2*pi))*e^((-1/2)*((Number of Successes-Mean of Normal Distribution)/Standard Deviation of Normal Distribution)^2)
P_Normal = 1/(σ_Normal*sqrt(2*pi))*e^((-1/2)*((x-μ_Normal)/σ_Normal)^2)
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 Probability Distribution Function - Normal Probability Distribution Function also known as the Gaussian distribution, is a mathematical function that describes a symmetrical bell-shaped curve.
Standard Deviation of Normal Distribution - Standard Deviation of Normal Distribution is the average distance between each data point and the mean of the distribution, providing a measure of how much the values typically deviate from the mean.
Number of Successes - Number of Successes is the random variable that denotes the number of events or occurrences within a fixed interval of time or space.
Mean of Normal Distribution - Mean of Normal Distribution is the average or expected value, and represents the central tendency of the distribution.

STEP 1: Convert Input(s) to Base Unit

Standard Deviation of Normal Distribution: 2 --> No Conversion Required
Number of Successes: 7 --> No Conversion Required
Mean of Normal Distribution: 5.5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_Normal = 1/(σ_Normal*sqrt(2*pi))*e^((-1/2)*((x-μ_Normal)/σ_Normal)^2) --> 1/(2*sqrt(2*pi))*e^((-1/2)*((7-5.5)/2)^2)

Evaluating ... ...

P_Normal = 0.150568716077402

STEP 3: Convert Result to Output's Unit

0.150568716077402 --> No Conversion Required

FINAL ANSWER

0.150568716077402 ≈ 0.150569 <-- Normal Probability Distribution Function

(Calculation completed in 00.004 seconds)

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Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< 2 Normal Distribution Calculators

Normal Probability Distribution

Go Normal Probability Distribution Function = 1/(Standard Deviation of Normal Distribution*sqrt(2*pi))*e^((-1/2)*((Number of Successes-Mean of Normal Distribution)/Standard Deviation of Normal Distribution)^2)

Z Score in Normal Distribution

Go Z Score in Normal Distribution = (Individual Value in Normal Distribution-Mean in Normal Distribution)/Standard Deviation in Normal Distribution

Normal Probability Distribution Formula

What is Probability?

In Mathematics, Probability theory is the study of chances. In real life, we predict chances depending on the situation. But Probability theory is bringing a mathematical foundation for the concept of Probability. For example, if a box contain 10 balls which include 7 black balls and 3 red balls and randomly chosen one ball. Then the Probability of getting red ball is 3/10 and Probability of getting black ball is 7/10. When coming to statistics, Probability is like the back bone of statistics. It has a wide application in decision making, data science, business trend studies, etc.

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 Probability Distribution?

Normal Probability Distribution calculator uses Normal Probability Distribution Function = 1/(Standard Deviation of Normal Distribution*sqrt(2*pi))*e^((-1/2)*((Number of Successes-Mean of Normal Distribution)/Standard Deviation of Normal Distribution)^2) to calculate the Normal Probability Distribution Function, The Normal Probability Distribution formula is defined as the likelihood of a continuous random variable falling within a specific range (usually defined by a mean and standard deviation). It is characterized by a symmetrical and bell-shaped curve and models the probability of observing a value within a range, assuming a normal or approximately normal distribution of the data. Normal Probability Distribution Function is denoted by P_Normal symbol.

How to calculate Normal Probability Distribution using this online calculator? To use this online calculator for Normal Probability Distribution, enter Standard Deviation of Normal Distribution (σ_Normal), Number of Successes (x) & Mean of Normal Distribution (μ_Normal) and hit the calculate button. Here is how the Normal Probability Distribution calculation can be explained with given input values -> 0.150569 = 1/(2*sqrt(2*pi))*e^((-1/2)*((7-5.5)/2)^2).

FAQ

What is Normal Probability Distribution?

The Normal Probability Distribution formula is defined as the likelihood of a continuous random variable falling within a specific range (usually defined by a mean and standard deviation). It is characterized by a symmetrical and bell-shaped curve and models the probability of observing a value within a range, assuming a normal or approximately normal distribution of the data and is represented as P_Normal = 1/(σ_Normal*sqrt(2*pi))*e^((-1/2)*((x-μ_Normal)/σ_Normal)^2) or Normal Probability Distribution Function = 1/(Standard Deviation of Normal Distribution*sqrt(2*pi))*e^((-1/2)*((Number of Successes-Mean of Normal Distribution)/Standard Deviation of Normal Distribution)^2). Standard Deviation of Normal Distribution is the average distance between each data point and the mean of the distribution, providing a measure of how much the values typically deviate from the mean, Number of Successes is the random variable that denotes the number of events or occurrences within a fixed interval of time or space & Mean of Normal Distribution is the average or expected value, and represents the central tendency of the distribution.

How to calculate Normal Probability Distribution?

The Normal Probability Distribution formula is defined as the likelihood of a continuous random variable falling within a specific range (usually defined by a mean and standard deviation). It is characterized by a symmetrical and bell-shaped curve and models the probability of observing a value within a range, assuming a normal or approximately normal distribution of the data is calculated using Normal Probability Distribution Function = 1/(Standard Deviation of Normal Distribution*sqrt(2*pi))*e^((-1/2)*((Number of Successes-Mean of Normal Distribution)/Standard Deviation of Normal Distribution)^2). To calculate Normal Probability Distribution, you need Standard Deviation of Normal Distribution (σ_Normal), Number of Successes (x) & Mean of Normal Distribution (μ_Normal). With our tool, you need to enter the respective value for Standard Deviation of Normal Distribution, Number of Successes & Mean of Normal 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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