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" (C. Friend, V. Bennett, and A. Nutman, Contrib Mineral Petrol, 2002:71-92) describes the chemical compositions of certain minerals in the early Archaean mantle. For a certain type of olivine assembly, the silicon dioxide (SiO2) 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 SiO2 content in a random sample of 10 rocks.
b. How many rocks must be sampled so that the standard deviation of the sample mean SiO2 content is 0.05?