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 such that:
, for any and .
Thank you very much in advance!