Standard Deviation of Binomial Distribution Calculator

✖Number of Trials is the total number of repetitions of a particular random experiment, under similar circumstances.ⓘ Number of Trials [N_Trials]			+10% -10%
✖Probability of Success is the probability of a specific outcome occurring in a single trial of a fixed number of independent Bernoulli trials.ⓘ Probability of Success [p]			+10% -10%
✖Probability of Failure in Binomial Distribution is the probability of a specific outcome not occurring in a single trial of a fixed number of independent Bernoulli trials.ⓘ Probability of Failure in Binomial Distribution [q_BD]			+10% -10%

✖Standard Deviation in Normal Distribution is the square root of expectation of the squared deviation of the given normal distribution following data from its population mean or sample mean.ⓘ Standard Deviation of Binomial Distribution [σ]

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Standard Deviation of Binomial Distribution

Formula

`"σ" = sqrt("N"_{"Trials"}*"p"*"q"_{"BD"})`

Example

`"1.549193"=sqrt("10"*"0.6"*"0.4")`

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Standard Deviation of Binomial Distribution Solution

STEP 0: Pre-Calculation Summary

Formula Used

Standard Deviation in Normal Distribution = sqrt(Number of Trials*Probability of Success*Probability of Failure in Binomial Distribution)
σ = sqrt(N_Trials*p*q_BD)
This formula uses 1 Functions, 4 Variables

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

Standard Deviation in Normal Distribution - Standard Deviation in Normal Distribution is the square root of expectation of the squared deviation of the given normal distribution following data from its population mean or sample mean.
Number of Trials - Number of Trials is the total number of repetitions of a particular random experiment, under similar circumstances.
Probability of Success - Probability of Success is the probability of a specific outcome occurring in a single trial of a fixed number of independent Bernoulli trials.
Probability of Failure in Binomial Distribution - Probability of Failure in Binomial Distribution is the probability of a specific outcome not occurring in a single trial of a fixed number of independent Bernoulli trials.

STEP 1: Convert Input(s) to Base Unit

Number of Trials: 10 --> No Conversion Required
Probability of Success: 0.6 --> No Conversion Required
Probability of Failure in Binomial Distribution: 0.4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ = sqrt(N_Trials*p*q_BD) --> sqrt(10*0.6*0.4)

Evaluating ... ...

σ = 1.54919333848297

STEP 3: Convert Result to Output's Unit

1.54919333848297 --> No Conversion Required

FINAL ANSWER

1.54919333848297 ≈ 1.549193 <-- Standard Deviation in Normal Distribution

(Calculation completed in 00.004 seconds)

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Home » Math » Probability and Disribution » Distribution » Binomial Distribution » Standard Deviation of Binomial Distribution

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< 8 Binomial Distribution Calculators

Binomial Probability Distribution

Go Binomial Probability = (C(Total Number of Trials,Number of Successful Trials))*Probability of Success in Binomial Distribution^Number of Successful Trials*Probability of Failure^(Total Number of Trials-Number of Successful Trials)

Standard Deviation of Negative Binomial Distribution

Go Standard Deviation in Normal Distribution = sqrt(Number of Success*Probability of Failure in Binomial Distribution)/Probability of Success

Standard Deviation of Binomial Distribution

Go Standard Deviation in Normal Distribution = sqrt(Number of Trials*Probability of Success*Probability of Failure in Binomial Distribution)

Mean of Negative Binomial Distribution

Go Mean in Normal Distribution = (Number of Success*Probability of Failure in Binomial Distribution)/Probability of Success

Variance of Negative Binomial Distribution

Go Variance of Data = (Number of Success*Probability of Failure in Binomial Distribution)/(Probability of Success^2)

Variance of Binomial Distribution

Go Variance of Data = Number of Trials*Probability of Success*Probability of Failure in Binomial Distribution

Variance in Binomial Distribution

Go Variance of Data = Number of Trials*Probability of Success*(1-Probability of Success)

Mean of Binomial Distribution

Go Mean in Normal Distribution = Number of Trials*Probability of Success

Standard Deviation of Binomial Distribution Formula

Standard Deviation in Normal Distribution = sqrt(Number of Trials*Probability of Success*Probability of Failure in Binomial Distribution)
σ = sqrt(N_Trials*p*q_BD)

What is Binomial Distribution?

A Binomial Distribution is a probability distribution that describes the number of successful outcomes in a fixed number of independent trials. Each trial has only two possible outcomes, typically labeled "success" and "failure".
The Binomial Distribution is defined by two parameters: the probability of success (p) in a single trial, and the number of trials (n).
The probability of getting exactly k successful outcomes in n trials is given by the binomial probability formula. P(x) = (n choose x) * (p^x) * ((1-p)^(n-x))

It is also a discrete probability distribution, and is used to model the number of successes in a fixed number of Bernoulli trials with a fixed probability of success.

How to Calculate Standard Deviation of Binomial Distribution?

Standard Deviation of Binomial Distribution calculator uses Standard Deviation in Normal Distribution = sqrt(Number of Trials*Probability of Success*Probability of Failure in Binomial Distribution) to calculate the Standard Deviation in Normal Distribution, Standard Deviation of Binomial Distribution formula is defined as the square root of expectation of the squared deviation of the random variable that follows Binomial distribution, from its mean. Standard Deviation in Normal Distribution is denoted by σ symbol.

How to calculate Standard Deviation of Binomial Distribution using this online calculator? To use this online calculator for Standard Deviation of Binomial Distribution, enter Number of Trials (N_Trials), Probability of Success (p) & Probability of Failure in Binomial Distribution (q_BD) and hit the calculate button. Here is how the Standard Deviation of Binomial Distribution calculation can be explained with given input values -> 1.549193 = sqrt(10*0.6*0.4).

FAQ

What is Standard Deviation of Binomial Distribution?

Standard Deviation of Binomial Distribution formula is defined as the square root of expectation of the squared deviation of the random variable that follows Binomial distribution, from its mean and is represented as σ = sqrt(N_Trials*p*q_BD) or Standard Deviation in Normal Distribution = sqrt(Number of Trials*Probability of Success*Probability of Failure in Binomial Distribution). Number of Trials is the total number of repetitions of a particular random experiment, under similar circumstances, Probability of Success is the probability of a specific outcome occurring in a single trial of a fixed number of independent Bernoulli trials & Probability of Failure in Binomial Distribution is the probability of a specific outcome not occurring in a single trial of a fixed number of independent Bernoulli trials.

How to calculate Standard Deviation of Binomial Distribution?

Standard Deviation of Binomial Distribution formula is defined as the square root of expectation of the squared deviation of the random variable that follows Binomial distribution, from its mean is calculated using Standard Deviation in Normal Distribution = sqrt(Number of Trials*Probability of Success*Probability of Failure in Binomial Distribution). To calculate Standard Deviation of Binomial Distribution, you need Number of Trials (N_Trials), Probability of Success (p) & Probability of Failure in Binomial Distribution (q_BD). With our tool, you need to enter the respective value for Number of Trials, Probability of Success & Probability of Failure in Binomial Distribution and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Standard Deviation in Normal Distribution?

In this formula, Standard Deviation in Normal Distribution uses Number of Trials, Probability of Success & Probability of Failure in Binomial Distribution. We can use 1 other way(s) to calculate the same, which is/are as follows -

Standard Deviation in Normal Distribution = sqrt(Number of Success*Probability of Failure in Binomial Distribution)/Probability of Success

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