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

Credits

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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12 Industrial Parameters Calculators

Binomial Distribution
Go Binomial Distribution = Number of Trials!*(Probability of Success of Single Trial^Specific Outcomes within Trials)*(Probability of Failure of Single Trial^(Number of Trials-Specific Outcomes within Trials))/(Specific Outcomes within Trials!*(Number of Trials-Specific Outcomes within Trials)!)
Normal Distribution
Go Normal Distribution = e^(-(Specific Outcomes within Trials-Mean of Distribution)^2/(2*Standard Deviation of distribution^2))/(Standard Deviation of distribution*sqrt(2*pi))
Learning Factor
Go Learning Factor = (log10(Time for Task 1)-log10(Time for n Tasks))/log10(Number of Tasks)
Poisson Distribution
Go Poisson Distribution = Mean of Distribution^(Specific Outcomes within Trials)*e^(-Mean of Distribution)/(Specific Outcomes within Trials!)
Annual Devaluation Rate
Go Annual Devaluation Rate = (Rate of Return Foreign Currency-Rate of Return USD)/(1+Rate of Return USD)
Crashing
Go Cost Slope = (Crash Cost-Normal Cost)/(Normal Time-Crash Time)
Forecasting Error
Go Forecasting Error = Observed Value at Time t-Smooth Averaged Forecast for Period t
Macroscopic Traffic Density
Go Traffic Density in vpm = Hourly Flow Rate in vph/(Avg. Travel Speed/0.277778)
General Sewing Data
Go GSD = (Man Power*Work Hours)/Target
Traffic Intensity
Go Traffic Intensity = Mean Arrival Rate/Mean Service Rate
Variance
Go Variance = ((Pessimistic Time-Optimistic Time)/6)^2
Reorder Point
Go Reorder Point = Lead Time Demand+Safety Stock

Normal Distribution 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))
Pnormal = e^(-(x-μ)^2/(2*σ^2))/(σ*sqrt(2*pi))

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 Pnormal 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 Pnormal = 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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