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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.
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Samuel Chukwuemeka

(Samdom For Peace)

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

Probability Distribution

Given: $x$, $P(x)$
(Enter data values horizontally)

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

$P(x)$ =

$x * P(x)$ =

$\mu = \Sigma [x * P(x)]$ =

$x^2$ =

$x^2 * P(x)$ =

$\Sigma(x^2 * P(x))$ =

$\mu^2$ =

$\Sigma[x^2 * P(x)] - \mu^2$ =

$\sigma$ =

Probability Distribution

Given: $x$, $P(x)$
(Enter data values vertically)

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

$P(x)$ =

$x * P(x)$ =

$\mu = \Sigma [x * P(x)]$ =

$x^2$ =

$x^2 * P(x)$ =

$\Sigma(x^2 * P(x))$ =

$\mu^2$ =

$\Sigma[x^2 * P(x)] - \mu^2$ =

$\sigma$ =

Empirical Rule

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

$\sigma$ =

Chebyshev's Theorem

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

$\sigma$ =

$k$ =

Uniform Distribution

Given: min, max, $x$
To Find: $P(x)$, other details
min =

max =

$x$ =

Uniform Distribution

Given: min, max, $x_1$, $x_2$
To Find: $P(x)$, other details
min =

max =

between and

Binomial Probability Distribution

Given: $x$, $n$, $p$
To Find: detailed $P(x)$, $q$, $\mu$, $\sigma$
$x$ =

$n$ =

$p$ =

Binomial Probability Distribution

Given: $n$, $p$
To Find: $q$, $\mu$, $\sigma$, min, max
$n$ =

$p$ =

Given: $P(x)$, $x$, $n$, $p$
To Find: $q$, $\mu$, $\sigma$
$P(x)$ =

$x$ =

$n$ =

$p$ =

Given: $P(x)$, $x$, $n$, $q$
To Find: $p$, $\mu$, $\sigma$
$P(x)$ =

$x$ =

$n$ =

$q$ =

Given: $n$, $q$
To Find: $p$, $\mu$, $\sigma$, min, max
$n$ =

$q$ =

Given: $\mu$, $\sigma$
To Find: $q$, $p$, $n$, max, min
$\mu$ =

$\sigma$ =

Poisson Probability Distribution

Given: $x$, $n$
To Find: $\mu$, $\sigma$, $\sigma^2$
$\Sigma x$ =

$n$ =

Poisson Probability Distribution

Given: $n$, $P(x)$
To Find: $\mu$ (or $E$), $\sigma$, $\sigma^2$
$n$ =

$P(x)$ =

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

$\mu$ =

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

$\sigma$ =

Poisson Distribution to Approximate Binomial Distribution

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

Given: $x$, $n$, $p$
To Find: $P(x)$, $\mu$, $\sigma$
$x$ =

$n$ =

$p$ =

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
$x$ =

$n$ =

$\sigma$ =

Normal Probability Distribution

Given: $z$
To Find: detailed $P(z)$
$z$ =

Normal Probability Distribution

Given: $z_1$, $z_2$ where $z_1 \le z_2$
To Find: detailed $P(z)$
$z_1$ =

$z_2$ =

Given: $x$, $\mu$, $\sigma$
To Find: $z$, detailed $P(z)$, $P(x)$
$x$ =

$\mu$ =

$\sigma$ =

Given: $x_1$, $x_2$ where $x_1 \le x_2$, $\mu$, $\sigma$
To Find: $z_1$, $z_2$, detailed $P(z)$, $P(x)$
$x_1$ =

$x_2$ =

$\mu$ =

$\sigma$ =

Normal Distribution to Approximate Binomial Distribution

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

Given: $n$, $p$
To Find: $q$, $\mu$, $\sigma$
$n$ =

$p$ =

Normal Distribution to Approximate Binomial Distribution

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

Given: $n$, $p$, detailed $x$
To Find: $q$, $\mu$, $\sigma$, $z$, $P(z)$, $P(x)$
$n$ =

$p$ =

$x$ =

Inverse Normal Distribution

Given: Left $P(z)$
To Find: $z$
$P(z)$ =

Inverse Normal Distribution

Given: Right $P(z)$
To Find: $z$
$P(z)$ =

Inverse Normal Distribution

Given: $\mu$, $\sigma$, Left $P(z)$
To Find: $z$, $x$
$\mu$ =

$\sigma$ =

$P(z)$ =

Inverse Normal Distribution

Given: $\mu$, $\sigma$, Right $P(z)$
To Find: $z$, $x$
$\mu$ =

$\sigma$ =

$P(z)$ =

Central Limit Theorem

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

Given: $x$, $\mu$, $\sigma$, $n$
To Find: $z$, detailed $P(z)$, $P(x)$
$x$ =

$\mu$ =

$\sigma$ =

$n$ =

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 $P(z)$, $P(x)$
$x_1$ =

$x_2$ =

$\mu$ =

$\sigma$ =

$n$ =