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
Final Answer
P(|X - μ| < kσ) ≥ 0.80246913580247
You have 2 free calculationss remaining
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?
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