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
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.
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
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
