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), variance (σ2), 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 Skewness | 0.1375 |
| 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
