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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