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In a population, the height (in cm) of a randomly selected adult is given by a random variable:
\(F\), with expectation \(E(F)=165\) and variance \(V(F)=25\) for a woman;
\(H\), with expectation \(E(H)=180\) and variance \(V(H)=36\) for a man.
Bound the probability \(P(|F-165|\ge 8)\).
Bound the probability that the height of a woman is \(\le 155\)~cm or \(\ge 175\)~cm.
Apply the Bienaymé--Tchebychev inequality to \(|H-180|\ge 10\) and interpret the result.
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