# P(x), μ, σ2, Skewness & Kurtosis for n = 18, P = 0.36 & X = 12 Solved example work with steps & calculation summary to estimate the probability of x number of successes P(x), mean (μ), variance2), standard deviation (σ), coefficient of skewness & coefficient of kurtosis of Binomial distribution for number of success X = 12, success probability for each trial P = 0.36 from the total number of events n = 18. The below is the Binomial distribution calculation summary for all the above parameters for n = 18, X = 12 & P = 0.36.
Calculation Summary
No. of finite events (n) 18
Probability of success/Trial (p)0.36
Negative probability (q)0.64
Number of success (x) 12
P(x)0.006
Mean (μ)6.48
Variance (σ2)4.1472
Standard deviation (σ)2.0365
Coefficient Skewness0.1375
Coefficient Kurtosis-0.0922

## Binomial Probability Distribution Workout for P(X = 12)

The below is the example work with steps shows how to estimate the probability of total number of x successes P(x) of Binomial distribution for n = 18, X = 12 & P = 0.36, may help grade school students to solve the such binomial probability worksheet problems efficiently.Workout
step 1 Address the formula, input parameters & values
Number of trials (n) = 18
Number of success (x) = 12
Success probability for each trial p = 0.36
P(x) = nCx px qn-x

step 2 Find combinations for 18 CHOOSE 12
18C12 = 18!/12!(18-12)!
= 18!/12! x 6!
= 6402373705728000/479001600720
18C12 = 18564

step 3 Find q value from p
q = 1 - p
q = 1 - 0.36
q = 0.64

step 4 Apply 18C12, p & q values in binomial distribution formula
P(x) = 18564 x 0.3612 x 0.646

step 5 solve the expression
P(x) = 18564 x 0 x 0.0687
P(x) = 0.006
Thus 0.006 is the binomial probability of getting 12 successes from 18 total number of events with 0.36 success probability for each trial.

## Workout for μ, σ2, Skewness & Kurtosis for n = 18 & P = 0.36

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 = 18 & P = 0.36, 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 = 18
p = 0.36
q = 1 - p = 1 - 0.36
q = 0.64

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 = 18 x 0.36
μ = 6.48

σ2 = npq = 18 x 0.36 x 0.64
σ2 = 4.1472

σ = √npq = √4.1472
σ = 2.0365

step 3 Apply the values in Coefficient Skewness formula
Coefficient Skewness = q - p/σ
= 0.64 - 0.36/2.0365
= 0.28/2.0365
= 0.1375
Coefficient Skewness = 0.1375

step 4 Apply the values in Coefficient Kurtosis formula
Coefficient Kurtosis = 1 - 6pq/σ²
= 1 - 6 x 0.36 x 0.64/4.1472
= 1 - 1.3824/4.1472
= -0.3824/4.1472
= -0.0922
Coefficient Kurtosis = -0.0922 