Choose 1 of the 2 below:
What is the that x is within standard deviations of the mean
The probability that X is k standard deviations of the mean is

What is the probability that X is within

2.25 standard deviations of the mean?

##### Chebyshev's Formula

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

P(|X - μ| < kσ) ≥ 1 - (1/k2)

##### Plug in k = 2.25

 P(|X - μ| < 2.25σ) ≥ 1 - 1 2.252

 P(|X - μ| < 2.25σ) ≥ 1 - 1 5.0625

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

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/k2

For 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/k2
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
theorem
A statement provable using logic