Answer to Question #349582 in Statistics and Probability for Arjun hawian

Question

A quality control want to estimate the proportion of high quality goods out of a batch of products with a 90% confidence level and a margin of error of 5%. How may products must he tes

Answer 1

A 90% confidence interval has a z-score (a critical value) $z_c=1.6449.$

$$ME=z_c\times\sqrt{\dfrac{p(1-p)}{n}}$$ $$=1.6449\times\sqrt{\dfrac{0.5(1-0.5)}{n}}=0.05$$ $$n=(16.449)^2$$ $$n=271$$