More than two standard deviations away from its mean

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SUMMARY

The discussion focuses on calculating the probability that a binomial random variable, specifically with parameters n = 100 and p = 0.5, is more than two standard deviations away from its mean. The expression P(|X - μ| > 2σ) is used to define this probability, where X represents the random variable, μ is the mean, and σ is the standard deviation. Additionally, the conversation references Chebyshev's Theorem as a method for establishing an upper bound for this probability. The participants seek clarity on the interpretation and solution of such statistical problems.

PREREQUISITES
  • Understanding of binomial distributions and their parameters (n and p).
  • Knowledge of mean (μ) and standard deviation (σ) in statistics.
  • Familiarity with Chebyshev's Theorem and its application in probability.
  • Basic proficiency in probability notation and concepts.
NEXT STEPS
  • Study the properties of binomial distributions, focusing on mean and variance calculations.
  • Learn how to apply Chebyshev's Theorem to various probability distributions.
  • Explore the concept of standard deviations in relation to normal distributions.
  • Practice solving problems involving P(|X - μ| > kσ) for different values of k.
USEFUL FOR

Statisticians, data analysts, students studying probability theory, and anyone interested in understanding binomial distributions and their properties.

Hiche
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more than "two standard deviations away from its mean"

Suppose we need to find the probability that a binomial random variable with n = 100 and p = 0.5 is more than two standard deviations away from its mean and then compare this to the upper bound given by Chebyshev's Theorem.

What is exactly meant by "more than two standard deviations away from its mean"? How do we exactly solve those kinds of problems? I'm rusty with this, so bear with me.
 
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Hey Hiche.

This means that you are finding P(|X - mu| > 2*sigma) where X is your random variable.
 

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