Ex$1$: Intel i$7$ processors come in different speeds: $2\mathrm{.}5GHz,3\mathrm{.}1GHz,3\mathrm{.}4$ GHz $,$ and $3\mathrm{.}5$ GHz $\mathrm{.}200$ processors are randomly selected and tested. $42$ of them are clocked at $3\mathrm{.}5$ GHz $.$ What is the $95\%$ confidence interval for the proportion of $3\mathrm{.}5$ GHz processors?