(p. 272). Recall that the time, x, between failures of the scanner is exponentially distributed with m = 40 days and s = 40 days. Now consider a random sample of n = 25 incidents of scanner failure, and let x represent the sample mean time between failures.

a. Find E(x) and Var(x).

b. Although x has an exponential distribution, the sampling distribution of x is approximately normal. Why?

c. Find the probability that the sample mean time between failures of the MRI scanner is less than 32 days.