1. Let Y be b(300, p). If the observed value of Y is y = 75, find an approximate 90 percent confidence interval for p.
2. Let X be the mean of a random sample of size n from a distribution that is N(µ, u2), where the positive variance u2 is known. Use the fact that (1)(2) - Cl>( -}) = 0.954 to find, for each µ, c1(µ) and c2 (µ) such that Pr [c1(µ) X c2 (µ)] = 0.954. Note that c1(µ) and c2 (µ) are increasing functions of µ. Solve for the respective functions d1(i) and d2(i); thus we also have that Pr [di{ X ) µ d1(X)] = 0.954. Compare this with the answer obtained previously in the text.