Binomial Probability
No. of finite events (n) :

Trial Probability (P) :

No. of success (x) :

Binomial probability P(X) :

Mean μ :

Variance σ2 :

Standard deviation σ :

Coefficient Skewness :

Coefficient Kurtosis :

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HISTORY

μ, σ2, Skewness & Kurtosis for n = 6 & P = 0.81

Solved example work with steps & calculation summary to estimate the probability, mean (μ), variance2), standard deviation (σ), coefficient of skewness & coefficient of kurtosis of Binomial distribution for success probability for each trial P = 0.81 from the total number of combinations n = 6. The below is the Binomial distribution calculation summary for all the above parameters for n = 6 & P = 0.81.
Calculation Summary
No. of finite events (n) 6
Probability of success/Trial (p)0.81
Negative probability (q)0.19
Mean (μ)4.86
Variance (σ2)0.9234
Standard deviation (σ)0.9609
Coefficient Skewness-0.6452
Coefficient Kurtosis0.083

Binomial Probability Distribution Workout for n = 6 & P = 0.81

The below is the example work with steps shows how to estimate the μ, σ2, σ, coefficient of skewness & coefficient of kurtosis of Binomial distribution for n = 6 & P = 0.81, may help grade school students to solve the such binomial probability worksheet problems efficiently.Workout
step 1 Address formula, input parameters & values.
Input parameters
n = 6
p = 0.81
q = 1 - p = 1 - 0.81
q = 0.19

Formula
Mean μ = np

Variance σ2 = npq

Standard Deviation σ = = √npq

Coefficient Skewness = q - p/σ
Coefficient Kurtosis = 1 - 6pq/σ²

step 2 Use n, p and q values to find mean, variance and standard deviation
μ = np = 6 x 0.81
μ = 4.86

σ2 = npq = 6 x 0.81 x 0.19
σ2 = 0.9234

σ = √npq = √0.9234
σ = 0.9609

step 3 Apply the values in Coefficient Skewness formula
Coefficient Skewness = q - p/σ
= 0.19 - 0.81/0.9609
= -0.62/0.9609
= -0.6452
Coefficient Skewness = -0.6452

step 4 Apply the values in Coefficient Kurtosis formula
Coefficient Kurtosis = 1 - 6pq/σ²
= 1 - 6 x 0.81 x 0.19/0.9234
= 1 - 0.9234/0.9234
= 0.0766/0.9234
= 0.083
Coefficient Kurtosis = 0.083