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**zadir** A fraction p of citizens in a city smoke. We are to determine the value of p by making a survey that involves n citizens whom we select randomly. If k of these n people smoke, then p'=k/n will be our result. How large should we choose n if we want our result p' to be closer to the real value p than 0.005 with probability at least 0.95? In other words: determine the smallest number $\displaystyle n_0$ such that:

$\displaystyle P(|p'-p|)\leq 0.005)\geq 0.95$, for any $\displaystyle p \in (0,1)$ and $\displaystyle n\geq n_0$.

Thank you very much in advance!