Sampling Distributions · Challenge problem

A buyer inspects a random sample of $100$ items from each large lot and rejects the lot if the sample proportion $\hat p$ of defectives exceeds a cutoff $c$. The cutoff is chosen so that a good lot, with $10\%$ defective, is rejected with probability $0.05$ (use the normal model for $\hat p$ with $z = 1.645$). What is the probability that a bad lot, with $20\%$ defective, is ACCEPTED? Use the normal model again and give your answer to four decimal places.