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A local population consist of 80% women and 20% men. If we select a sample of 20 people at random from this population, then how many woman can we expect to be selected in the sample?

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Any random sample from the population will still be $80$ percent women and $20$ percent men. What's $80$ percent of $20$?

\begin{align*} .80(20) = 16 \end{align*}

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  • $\begingroup$ this needs an "in expectation" somewhere. Certainly not every random sample will be 80 percent women and 20 percent men. $\endgroup$ – WetlabStudent Feb 28 '15 at 1:07
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To show the answer using formal computation of expected values,

If X is any one person from the population, then all we know from the problem is. $$ p(X = woman) = 0.8 $$ so $$ E(\sum_{i=1}^{20}\delta(X_i = woman)) = \sum_{i=1}^{20}E(\delta(X_i = woman)) $$ $$ = \sum_{i=1}^{20}p(X_i = woman) = \sum_{i=1}^{20}0.8 = 16$$

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