Chebyshev on a concrete interval
A random variable has mean and standard deviation (nothing else is known about its shape). Using Chebyshev's inequality, find the smallest half-width such that the interval is guaranteed to contain at least of the probability. (to the nearest integer)
Show hints (2)+
- 96% inside means at most 4% outside; set Chebyshev's bound 1/k^2 = 0.04 and solve for k.
- k comes out in standard deviations (k = 5), so the half-width is c = k * sigma = 5 * 5.
Answer
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