where the rv the number of successes in independent trials with probability of success in a single trial of . Now given the title of this thread I assume we are supposed to use a normal approximation to the binomial to do this, in which case we have:
of the probabilty mass of a normal RV is contained within standard deviations of the mean, so if we have:
which will allow you to find the smallest for which this is true.
Now you can do the case where yourself.