Uranium in the Earth’s crust. Refer to the American Mineralogist (Oct. 2009) study of the evolution of uranium minerals in the Earth’s crust, Exercise 5.9

(p. 266). Recall that researchers estimate that the trace amount of uranium x in reservoirs follows a uniform distribution ranging between 1 and 3 parts per million. In a random sample of n = 60 reservoirs, let x represent the sample mean amount of uranium.

a. Find E1x2 and interpret its value.

b. Find Var(x).

c. Describe the shape of the sampling distribution of x.

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

e. Find the probability that x exceeds 2.2 ppm.