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What is the probability that is at most the observed value

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 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 .

(b) What distribution does follow?

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