# Chebyshev’s Rule Calculator

Instructions: This Chebyshev's Rule calculator will show you how to use Chebyshev's Inequality to estimate probabilities of an arbitrary distribution. You can estimate the probability that a random variable $$X$$ is within $$k$$ standard deviations of the mean, by typing the value of $$k$$ in the form below; OR specify the population mean $$\mu$$, population standard deviation $$\sigma$$ and the even $$(a,b)$$ for which you want to estimate the probability: Type of the value of k (number of standard deviations from the mean)

OR: Population Mean ($$\mu$$) Population St. Dev. ($$\sigma$$) Lower Limit of the event $$(a)$$: Upper Limit of the event $$(b)$$:

## More About the Chebyshev's Inequality Calculator

We use Chebyshev's inequality to compute the probability that $$X$$ is within $$k$$ standard deviations of the mean. According to Chebyshev's rule, the probability that $$X$$ is within $$k$$ standard deviations of the mean can be estimated as follows:

$\Pr(|X - \mu| < k \sigma) \ge 1 - \frac{1}{k^2}$

Chebyshev's inequality is very powerful, because it applies to any generic distribution. If you are dealing with a normal distribution, you should use our empirical rule instead.

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