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Probability Inequalities are useful for bounding quantities that might otherwise be hard to compute. A related concept is a concentration inequality, which specifically provides bounds on how far a random variable deviates from some value.
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Chebyshev's Inequality
A certain type of light bulb has an average lifetime of 10,000 hours. The SD of bulb lifetimes is 470 hours. What fraction of bulbs could last more than 10,705 hours?
I think the correct answer should …