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

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.
For some calculations, you may need to refresh your browser for each new calculation.
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 Chukwuemeka

(Samdom For Peace)

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

• ## Symbols and Meanings

• $x$ = variable
• $P(x)$ = probability of the variable
• $\mu$ = mean
• $\sigma$ = standard deviation
• $\Sigma$ = sigma (means summation)
• $k$ = number of standard deviations of the mean
• $min$ = minimum data value
• $max$ = maximum data value
• $x_1$ = first value of the variable
• $x_2$ = second value of the variable
• $n$ = sample size
• $N$ = population size
• $p$ = probability of success
• $q$ = probability of failure
• $E$ = expected value
• $z$ = z-score
• $z_1$ = first value of the z-score
• $z_2$ = second value of the z-score
• $P(z)$ = probability of the z-score

## Probability Distribution

• Given: $x$, $P(x)$

To Find: $\mu$, $\sigma$ (Show all steps), other details

## Empirical Rule

• Given: $\mu$, $\sigma$

To Find: detailed $P(x)$

## Chebyshev's Theorem

• Given: $\mu$, $\sigma$, $k$

To Find: $P(x)$

## Uniform Distribution

• Given: min, max, $x$

To Find: $P(x)$, other details

## Uniform Distribution

• Given: min, max, $x_1$, $x_2$

To Find: $P(x)$, other details

• between and

## Binomial Probability Distribution

• Given: $x$, $n$, $p$

To Find: detailed $P(x)$, $q$, $\mu$, $\sigma$

## Binomial Probability Distribution

• Given: $n$, $p$

To Find: $q$, $\mu$, $\sigma$, min, max

• Given: $P(x)$, $x$, $n$, $p$

To Find: $q$, $\mu$, $\sigma$

• Given: $P(x)$, $x$, $n$, $q$

To Find: $p$, $\mu$, $\sigma$

• Given: $n$, $q$

To Find: $p$, $\mu$, $\sigma$, min, max

• Given: $\mu$, $\sigma$

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

## Poisson Probability Distribution

• Given: $x$, $n$

To Find: $\mu$, $\sigma$, $\sigma^2$

## Poisson Probability Distribution

• Given: $n$, $P(x)$

To Find: $\mu$ (or $E$), $\sigma$, $\sigma^2$

• Given: $x$, $\mu$

To Find: detailed $P(x)$, $\sigma$

• Given: $x$, $\sigma$

To Find: $\mu$, detailed $P(x)$

## Poisson Distribution to Approximate Binomial Distribution

When requirements are met: $n \ge 100$ and $np \le 10$

• Given: $x$, $n$, $p$

To Find: $P(x)$, $\mu$, $\sigma$

## Poisson Distribution to Approximate Binomial Distribution

When requirements are met: $n \ge 100$ and $np \le 10$

• Given: $x$, $n$, $\sigma$

To Find: $P(x)$, $\mu$, p

## Normal Probability Distribution

• Given: $z$

To Find: detailed $P(z)$

## Normal Probability Distribution

• Given: $z_1$, $z_2$ where $z_1 \le z_2$

To Find: detailed $P(z)$

• Given: $x$, $\mu$, $\sigma$

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

• Given: $x_1$, $x_2$ where $x_1 \le x_2$, $\mu$, $\sigma$

To Find: $z_1$, $z_2$, detailed $P(z)$, $P(x)$

## Normal Distribution to Approximate Binomial Distribution

When requirements are met: $np \ge 5$ and $nq \ge 5$

• Given: $n$, $p$

To Find: $q$, $\mu$, $\sigma$

## Normal Distribution to Approximate Binomial Distribution

When requirements are met: $np \ge 5$ and $nq \ge 5$

• Given: $n$, $p$, detailed $x$

To Find: $q$, $\mu$, $\sigma$, $z$, $P(z)$, $P(x)$

## Inverse Normal Distribution

• Given: Left $P(z)$

To Find: $z$

## Inverse Normal Distribution

• Given: Right $P(z)$

To Find: $z$

## Inverse Normal Distribution

• Given: $\mu$, $\sigma$, Left $P(z)$

To Find: $z$, $x$

## Inverse Normal Distribution

• Given: $\mu$, $\sigma$, Right $P(z)$

To Find: $z$, $x$

## Central Limit Theorem

When requirements are met:
$n \gt 30$ or $N$ is normally distributed

• Given: $x$, $\mu$, $\sigma$, $n$

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

## Central Limit Theorem

When requirements are met:
$n \gt 30$ or $N$ is normally distributed

• Given: $x_1$, $x_2$ where $x_1 \le x_2$, $\mu$, $\sigma$, $n$

To Find: $z_1$, $z_2$, detailed $P(z)$, $P(x)$