The article “Abyssal Peridotites > 3800 Ma from Southern West Greenland: Field Relationships, Petrography, Geochronology, Whole-Rock and Mineral Chemistry of Dunite and Harzburgite Inclusions in the Itsaq Gneiss Complex” describes the chemical compositions of certain mineralsin the early Archaean mantle. For a certain type of olivine assembly, the silicon dioxide () content (in weight percent) in a randomly chosen rock has mean 40.25 and standard deviation 0.36.

a. Find the mean and standard deviation of the sample mean content in a random sample of 10 rocks.

b. How many rocks must be sampled so that the standard deviation of the sample mean content is 0.05?




(a) Let ? = 40.25 be the mean content, and let ?= 0.36 be the standard deviation of the content, in a randomly chosen rock. Let be the average content in a random sample of 10 rocks.

Then and = ? = 40.25 and



(b) Let n be the required number of rocks. Then

Solving for n yields n = 51.84. Since n must be an integer, take n = 52.

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