Problem 8.29 Suppose you want to test H0: 50 against H1 : > 50 using a random sample of size n taken

Problem 8.29 Suppose you want to test H0: µ ≤ 50 against H1 : µ > 50 using a random sample of size n taken from a normal distribution N(µ, 81). Find the minimum sample size n and the cutoff value c if the probability of a type I error is to be α = 0.05 and the probability of a type II error at the alternative µ = 55 is to be β(55) = 0.20.