A manufacturer of boxes of candy is concerned about the proportion of imperfect boxes – those containing cracked, broken, or otherwise damaged candies. (a) How large a sample is needed to be 99% confident that the difference between the sample fraction of imperfect boxes and the population proportion of imperfect boxes is no more than .015? Assume here that we have absolutely no information concerning the true proportion of imperfect boxes. (b) How does your answer to part (a) change if we assume that the population proportion of imperfect boxes is at least .005 and no more than .1?