Refer to the American Mineralogist (October 2009) study of the evolution of uranium minerals in the Earth’s crust, Exercise. 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-bar represent the sample mean amount of uranium.
a. Find E(x-bar) and interpret its value.
b. Find Var(x-bar).
c. Describe the shape of the sampling distribution of x-bar.
d. Find the probability that x-bar is between 1.5 ppm and 2.5 ppm.
e. Find the probability that x exceeds 2.2 ppm.