$7\mathrm{.}29.$ A fraction nonconforming control chart is to be estahliched with at center tine of $0\mathrm{.}01$ ind two$-$sigma control limits$.$

$($a$)$ How large should the sample size be if the lower control limit is to be nonzero?

$($b$)$ How hirge thot it the cample vize be if we wash the probability of detecting a shift to $0\mathrm{.}04$ to be $0\mathrm{.}507$