8.60 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. Show your work. (c) Does the   Very Quick Rule work well here? Explain. (d) What sample size would be needed   to obtain an error of ± 0.04 with 90 percent confidence?         8.66 The   U.S. Customs Service conducted a random check of Miami longshoremen and found   that 36 of 50 had arrest records. (a) Construct a 90 percent confidence   interval for the true proportion. (b) Is the sample size large enough to be   convincing? Explain.