A hydrologist collects a liter of water from each of 80 random locations along a stream and measures the amount of dissolved oxygen in each specimen. Suppose that we know that dissolved oxygen varies among locations according to a normal distribution with mean of 5 milligrams per liter (mg/l) and standard deviation of 0.92. Let X be the average oxygen content of the 80 specimens. The observed mean is 4.62 mg/l.
(a) Find the mean and the standard deviation of X
(b) What distribution does X follow?
(c) What is the probability that X is at most the observed value of 4.62?