Suppose a certain oil producing country exports (1 + X) million barrels of oil per day, where X is a random variable having a normal distribution with mean zero and variance 1/25.

(a) Find the exact probability that in 16 days more than 17 million barrels of oil will be exported.

(b) If the exact distribution of X is unknown, but one knows that E[X] = 0 and Var[X] = 1/6, then find an approximation for the probability that in 36 days less than 35 million barrels of oil will be exported.

(c) Suppose that not only is the exact distribution of X unknown, but also E[X] and Var[X] are unknown. If a random sample of 36 days productions results in x = 1 million barrels of oil per day and s = 1/10 million barrels of oil per day, construct a 95% confidence interval for E[X].