The Probability that x is within k standard deviations of the mean

P(|X - μ| < kσ) ≥ 1 - (1/k^{2})

Plug in k = 2.25

P(|X - μ| < 2.25σ) ≥ 1 -

1

2.25^{2}

P(|X - μ| < 2.25σ) ≥ 1 -

1

5.0625

P(|X - μ| < kσ) ≥ 1 - 0.19753086419753

Final Answer

P(|X - μ| < kσ) ≥ 0.80246913580247

What is the Answer?

P(|X - μ| < kσ) ≥ 0.80246913580247

How does the Chebyshevs Theorem Calculator work?

Free Chebyshevs Theorem Calculator - Using Chebyshevs Theorem, this calculates the following: Probability that random variable X is within k standard deviations of the mean. How many k standard deviations within the mean given a P(X) value. This calculator has 2 inputs.

What 1 formula is used for the Chebyshevs Theorem Calculator?

P(|X - μ|) ≥ kσ) ≤ 1/k^{2For more math formulas, check out our Formula Dossier}

What 6 concepts are covered in the Chebyshevs Theorem Calculator?

absolute value

A positive number representing the distance from 0 on a number line

chebyshevs theorem

estimates the minimum proportion of observations that fall within a specified number of standard deviations from the mean. P(|X - μ|) ≥ kσ) ≤ 1/k^{2}

mean

A statistical measurement also known as the average

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