Question

A chemical reaction is run in which the usual yield is . A new process has been devised that should improve the yield. Proponents of new process claim that it produces a better yield than the old one more than of time. The new process is tested times. Let denote the number of trials in which yield exceeds and be the probability of an increased yield.
(i) Which distribution does follow?
(ii) Let the claim be accepted if . What is the probability that claim is accepted if is really only ? (use normal approximation).