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Normal Probability Distribution Formula

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Normal Probability Distribution Function also known as the Gaussian distribution, is a mathematical function that describes a symmetrical bell-shaped curve. Check FAQs

P Normal = \frac{1}{σ Normal \cdot \sqrt{2 \cdot π}} \cdot e^{(- \frac{1}{2}) \cdot {(\frac{x - μ Normal}{σ Normal})}^{2}}

P_Normal - Normal Probability Distribution Function?σ_Normal - Standard Deviation of Normal Distribution?x - Number of Successes?μ_Normal - Mean of Normal Distribution?π - Archimedes' constant?

Normal Probability Distribution Example

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

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

Here is how the Normal Probability Distribution equation looks like.

0.1506 = \frac{1}{2 \cdot \sqrt{2 \cdot 3.1416}} \cdot e^{(- \frac{1}{2}) \cdot {(\frac{7 - 5.5}{2})}^{2}}

0.1506 = \frac{1}{2 \cdot \sqrt{2 \cdot 3.1416}} \cdot e^{(- \frac{1}{2}) \cdot {(\frac{7 - 5.5}{2})}^{2}}

0.1506 = \frac{1}{2 \cdot \sqrt{2 \cdot 3.1416}} \cdot e^{(- \frac{1}{2}) \cdot {(\frac{7 - 5.5}{2})}^{2}}

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Normal Probability Distribution Solution

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

FIRST Step Consider the formula

P Normal = \frac{1}{σ Normal \cdot \sqrt{2 \cdot π}} \cdot e^{(- \frac{1}{2}) \cdot {(\frac{x - μ Normal}{σ Normal})}^{2}}

Next Step Substitute values of Variables

∴

P Normal = \frac{1}{2 \cdot \sqrt{2 \cdot π}} \cdot e^{(- \frac{1}{2}) \cdot {(\frac{7 - 5.5}{2})}^{2}}

Next Step Substitute values of Constants

∴

P Normal = \frac{1}{2 \cdot \sqrt{2 \cdot 3.1416}} \cdot e^{(- \frac{1}{2}) \cdot {(\frac{7 - 5.5}{2})}^{2}}

Next Step Prepare to Evaluate

∴

P Normal = \frac{1}{2 \cdot \sqrt{2 \cdot 3.1416}} \cdot e^{(- \frac{1}{2}) \cdot {(\frac{7 - 5.5}{2})}^{2}}

Next Step Evaluate

∴

P Normal = 0.150568716077402

LAST Step Rounding Answer

∴

P Normal = 0.1506

Normal Probability Distribution Formula Elements

Variables

Constants

Functions

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.

Symbol: P_Normal

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Normal Probability Distribution Function

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.

Symbol: σ_Normal

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Standard Deviation of Normal Distribution

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.

Symbol: x

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Successes

Mean of Normal Distribution

Mean of Normal Distribution is the average or expected value, and represents the central tendency of the distribution.

Symbol: μ_Normal

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mean of Normal 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)

Other formulas in Normal Distribution category

Go Z Score in Normal Distribution

Z = \frac{A - μ}{σ}

How to Evaluate Normal Probability Distribution?

Normal Probability Distribution evaluator 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 evaluate 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 evaluate Normal Probability Distribution using this online evaluator? To use this online evaluator 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.

FAQs on Normal Probability Distribution

What is the formula to find Normal Probability Distribution?

The formula of Normal Probability Distribution is expressed as 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). Here is an example- 0.150569 = 1/(2*sqrt(2*pi))*e^((-1/2)*((7-5.5)/2)^2).

How to calculate Normal Probability Distribution?

With Standard Deviation of Normal Distribution (σ_Normal), Number of Successes (x) & Mean of Normal Distribution (μ_Normal) we can find Normal Probability Distribution using the formula - 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). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

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Normal Probability Distribution Formula

Normal Probability Distribution Example

Normal Probability Distribution Solution

Normal Probability Distribution Formula Elements

Other formulas in Normal Distribution category

How to Evaluate Normal Probability Distribution?

FAQs on Normal Probability Distribution

Variable Name