Let X be the number of defective parts produced in a given day in a manufacturin

Question

Let X be the number of defective parts produced in a given day in a manufacturing plant. For various values of positive constant C > 20, what is the best upper bound that you can give for P(X >= C) if you know (a) only that E(X) = 20, (b) that E(X) = 20 and Var(X) = 25, and finally (c) that E(X) = 20, Var(X) = 25, and X is symmetric about its mean? Thanks in advance for the help! I appreciate any help and I will review positively.

Explanation / Answer

X being symmetric about its mean just says that we can normalize X. So: P(X >= C) => P(X > 20) => P([X-20]5/ > (20-20)/5) => P(Z > 0) = 0.5

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