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(See Solution) For a randomly selected county in the United States, let X represent the proportion of adults over the age of 65 who are employed, or the

Question: For a randomly selected county in the United States, let \(X\) represent the proportion of adults over the age of 65 who are employed, or the elderly employment rate. Then, \(X\) is restricted to a value between zero and one. Suppose that the cumulative distribution function for \(\mathrm{X}\) is given by

\[F(x)=3 x^{2}-2 x^{3} \text { for } 0 \leq x \leq 1\]

Find the probability that the elderly employment rate is at least .6

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