# P(x), μ, σ^{2}, Skewness & Kurtosis for n = 18, P = 0.36 & X = 12

*probability*of x number of successes P(x),

*mean*(μ),

*variance*(σ

^{2}),

*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 (σ^{2}) | 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 p^{x} q^{n-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 0.36^{12} x 0.64^{6}

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, σ^{2}, Skewness & Kurtosis for n = 18 & P = 0.36

The below is the example work with steps shows how to estimate the μ, σ^{2}, 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 σ^{2} = 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

σ^{2} = npq = 18 x 0.36 x 0.64

σ^{2} = 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