A chemical reaction is run in which the usual yield is 70%. A new process has been devised that should improve the yield. Proponents of the new process claim that it produces better yields than the old process more than 90% of the time. The new process is tested 60 times. Let X denote the number of trials in which the yield exceeds 70%.
(a) If the probability of an increased yield is .9, is the normal approximation appropriate?
(b) If p = .9, what is E[X]?
(c) If p > .9 as claimed then, on the average, more than 54 of every 60 trials will result in an increased yield. Let us agree to accept the claim if X is at least 59. What is the probability that we will accept the claim if p is really only .9?
(d) What is the probability that we will not accept the claim (X < 58)="" if="" it="" is="" true,="" and="" p="" is="" really="">