Uranium in the Earth’s crust. In an American Mineralogist(October 2009) study of the evolu...

Uranium in the Earth’s crust. In an American Mineralogist(October 2009) study of the evolution of uranium minerals in the Earth’s crust, researchers estimated that the trace amount of uranium x in reservoirs follows a uniform distribution ranging between 1 and 3 parts per million. This distribution has mean μ = 2 ppm and variance σ2 = 1/3 ppm. In a random sample of n= 60 reservoirs, let   represent the sample mean amount of uranium.

a. Find E() and interpret its value.

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b. Find Var(). c. Describe the shape of the sampling distribution of .

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d. Find the probability that   is between 1.5 ppm and 2.5 ppm.

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e. Find the probability that   exceeds 2.2 ppm.