A binomial distribution has a probability of success = 0.1
Calculate the probability of exactly 4 successes in 12 trials:
The binomial probability formula is as follows:
| f(k;n,p) = | n! * pkqn - k | |
| k!(n - k)! |
Calculate q - the probability of failure:
q = 1 - p
q = 1 - 0.1
q = 0.9
Calculate n!:
n! = 12!
12! = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
12! = 479001600
Calculate k!:
k! = 4!
4! = 4 * 3 * 2 * 1
4! = 24
Calculate (n - k)!:
(n - k)! = (12 - 4)!
(n - k)! = 8!
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
8! = 40320
Calculate the binomial distribution probability:
| P(X = 4) = | 12! * 0.140.9(12 - 4) | |
| 4!(12 - 4)! |
| P(X = 4) = | 479001600 * 0.0001 * 0.98 | |
| 24 * 40320 |
| P(X = 4) = | 479001600 * 0.0001 * 0.43046721 | |
| 967680 |
| P(X = 4) = | 20619.448233754 | |
| 967680 |
Excel or Google Sheets formula:
Excel or Google Sheets formula:=BINOMDIST(4,12,0.1,FALSE)Calculate nq to see if we can use the Normal Approximation:
Since q = 1 - p, we have n(1 - p) = 12(1 - 0.1)
nq = 12(0.9)
nq = 10.8
Calculate the mean μ (expected value)
μ = np
μ = 12 x 0.1
μ = 1.2
Calculate the variance σ2
σ2 = np(1 - p)
σ2 = 12 x 0.1 x (1 - 0.1)
σ2 = 1.2 x 0.9
σ2 = 1.08
Calculate the standard deviation σ
σ = √σ2 = √np(1 - p)
σ = √1.08
σ = 1.0392
Calculate Skewness:
| Skewness = | 1 - 2p |
| √np(1 - p) |
| Skewness = | 1 - 2(0.1) |
| √12(0.1)(1 - 0.1) |
| Skewness = | 1 - 0.2) |
| √12(0.1)(0.9) |
| Skewness = | 0.8 |
| √1.08 |
Skewness = 0.74074074074074
Calculate Kurtosis:
| Kurtosis = | 1 - 6p(1 - p) |
| np(1 - p) |
| Kurtosis = | 1 - 6(0.1)(1 - 0.1) |
| 12(0.1)(1 - 0.1) |
| Kurtosis = | 1 - (0.6)(0.9) |
| 12(0.1)(0.9) |
| Kurtosis = | 1 - 0.54 |
| 1.08 |
| Kurtosis = | 0.46 |
| 1.08 |
Kurtosis = 0.42592592592593
Final Answer
Kurtosis = 0.42592592592593
You have 2 free calculationss remaining
What is the Answer?
Kurtosis = 0.42592592592593
How does the Binomial Distribution Calculator work?
Free Binomial Distribution Calculator - Calculates the probability of 3 separate events that follow a binomial distribution. It calculates the probability of exactly k successes, no more than k successes, and greater than k successes as well as the mean, variance, standard deviation, skewness and kurtosis.
Also calculates the normal approximation to the binomial distribution with and without the continuity correction factor
Calculates moment number t using the moment generating function
This calculator has 4 inputs.
Also calculates the normal approximation to the binomial distribution with and without the continuity correction factor
Calculates moment number t using the moment generating function
This calculator has 4 inputs.
What 3 formulas are used for the Binomial Distribution Calculator?
q = 1 - p
f(k;n,p) = n! * pkqn - k/k!(n - k)!
Z = X - np/√np(1 - p)
For more math formulas, check out our Formula Dossier
f(k;n,p) = n! * pkqn - k/k!(n - k)!
Z = X - np/√np(1 - p)
For more math formulas, check out our Formula Dossier
What 10 concepts are covered in the Binomial Distribution Calculator?
- binomial distribution
- discrete probability distribution of the number of successes in a sequence of n independent experiments, with a success or failure outcome
- continuity correction factor
- the bridge between the continuous normal distribution and the discrete binomial
- event
- a set of outcomes of an experiment to which a probability is assigned.
- factorial
- The product of an integer and all the integers below it
- mean
- A statistical measurement also known as the average
- moment
- a function are quantitative measures related to the shape of the functions graph
- probability
- the likelihood of an event happening. This value is always between 0 and 1.
P(Event Happening) = Number of Ways the Even Can Happen / Total Number of Outcomes - standard deviation
- a measure of the amount of variation or dispersion of a set of values. The square root of variance
- variance
- How far a set of random numbers are spead out from the mean
Example calculations for the Binomial Distribution Calculator
Binomial Distribution Calculator Video
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