More than two standard deviations away from its mean

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The discussion focuses on calculating the probability that a binomial random variable, with parameters n = 100 and p = 0.5, is more than two standard deviations away from its mean. This is expressed mathematically as P(|X - mu| > 2*sigma). Participants clarify the meaning of being "more than two standard deviations away" and emphasize the importance of understanding this concept for solving related problems. Additionally, there is a mention of comparing the calculated probability to the upper bound provided by Chebyshev's Theorem. The conversation aims to clarify the steps involved in these probability calculations.
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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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