A certain brand of dry noodles contains a mixture of beet, spinach, carrot, and plain. A random sample of 200 dry noodles contained 47 beet noodles.
(a) Construct a 95 percent confidence interval for the true proportion of beet noodles.
(b) Check the normality assumption for p. Show your work.
(c) What sample size would be needed to obtain an error of ±0.04 with 95 percent confidence?