For in GOD we live, and move, and have our being. - Acts 17:28

The Joy of a Teacher is the Success of his Students. - Samuel Dominic Chukwuemeka

Probability Distribution Calculators

Samuel Chukwuemeka teaching Statistics

I greet you this day,

You may use these calculators to check your answers. You are encouraged to solve the questions first, and check your answers. These topics are covered in my Notes and Videos on Probability Distributions. I wrote the codes for these calculators using Javascript, a client-side scripting language. Please use the latest Internet browsers. The calculators should work. Comments, ideas, areas of improvement, questions, and constructive criticisms are welcome. You may contact me. Please be positive if you do.
Thank you for visiting!!!

Samuel Dominic Chukwuemeka

Samuel Chukwuemeka

(Samdom For Peace)

B.Eng., A.A.T, M.Ed., M.S

Probability Distribution Empirical Rule Chebyshev's Theorem
Binomial Distribution Poisson Distribution Uniform Distribution
Normal Distribution Central Limit Theorem Geometric Distribution
Hypergeometric Distribution Notes and Videos Other Calculators

Probability Distribution

Given: x, P(x)

To Find: μ, σ (Show all steps), other details

Probability Distribution Empirical Rule Chebyshev's Theorem
Binomial Distribution Poisson Distribution Uniform Distribution
Normal Distribution Central Limit Theorem Geometric Distribution
Hypergeometric Distribution Notes and Videos Other Calculators

Empirical Rule

Given: μ, σ

To Find: detailed P(x)

Probability Distribution Empirical Rule Chebyshev's Theorem
Binomial Distribution Poisson Distribution Uniform Distribution
Normal Distribution Central Limit Theorem Geometric Distribution
Hypergeometric Distribution Notes and Videos Other Calculators

Chebyshev's Theorem

Binomial Probability Distribution

Given: x, n, p

To Find: detailed P(x), q, μ, σ

Given: n, p

To Find: q, μ, σ, min, max

Given: P(x), x, n, p

To Find: q, μ, σ

Given: P(x), x, n, q

To Find: p, μ, σ

Given: n, q

To Find: p, μ, σ, min, max

Given: μ, σ

To Find: q, p, n, max, min

Probability Distribution Empirical Rule Chebyshev's Theorem
Binomial Distribution Poisson Distribution Uniform Distribution
Normal Distribution Central Limit Theorem Geometric Distribution
Hypergeometric Distribution Notes and Videos Other Calculators

Poisson Probability Distribution

Given: x, n

To Find: μ, σ, σ2

Given: n, P(x)

To Find: μ (or E), σ, σ,2

Given: x, μ

To Find: detailed P(x), σ

Given: x, σ

To Find: μ, detailed P(x)

Poisson Distribution to Approximate Binomial Distribution

When requirements are met: n ≥ 100 and np ≤ 10

Given: x, n, p

To Find: P(x), μ, σ

Given: x, n, σ

To Find: P(x), μ, p

Probability Distribution Empirical Rule Chebyshev's Theorem
Binomial Distribution Poisson Distribution Uniform Distribution
Normal Distribution Central Limit Theorem Geometric Distribution
Hypergeometric Distribution Notes and Videos Other Calculators

Uniform Distribution

Given: min, max, x

To Find: P(x), other details

Given: min, max, x1, x2

To Find: P(x), other details

between and

Probability Distribution Empirical Rule Chebyshev's Theorem
Binomial Distribution Poisson Distribution Uniform Distribution
Normal Distribution Central Limit Theorem Geometric Distribution
Hypergeometric Distribution Notes and Videos Other Calculators

Normal Probability Distribution

Given: z

To Find: detailed P(z)

Given: z1, z2 where z1 ≤ z2

To Find: detailed P(z)

Given: x, μ, σ

To Find: z, detailed P(z), P(x)

Given: x1, x2 where x1 ≤ x2, μ, σ

To Find: z1, z2, detailed P(z), P(x)

Normal Distribution to Approximate Binomial Distribution

When requirements are met: np ≥ 5 and nq ≥ 5

Given: n, p

To Find: q, μ, σ

Given: n, p, detailed x

To Find: q, μ, σ, z, P(z), P(x)

Inverse Normal Distribution

Given: Left P(z)

To Find: z

Given: Right P(z)

To Find: z

Given: μ, σ, Left P(z)

To Find: z, x

Given: μ, σ, Right P(z)

To Find: z, x

Probability Distribution Empirical Rule Chebyshev's Theorem
Binomial Distribution Poisson Distribution Uniform Distribution
Normal Distribution Central Limit Theorem Geometric Distribution
Hypergeometric Distribution Notes and Videos Other Calculators

Central Limit Theorem

When requirements are met: n > 30 or N is normally distributed

Given: x, μ, σ, n

To Find: z, detailed P(z), P(x)

Given: x1, x2 where x1 ≤ x2, μ, σ, n

To Find: z1, z2, detailed P(z), P(x)

Probability Distribution Empirical Rule Chebyshev's Theorem
Binomial Distribution Poisson Distribution Uniform Distribution
Normal Distribution Central Limit Theorem Geometric Distribution
Hypergeometric Distribution Notes and Videos Other Calculators