41 Critical part failures in NASCAR vehicles. In The Sport Journal (Winter, 2007) analysis of critical part failures at NASCAR races, researchers found that the time x (in hours) until the first critical part failure is exponentially distributed with m = .10 and s = .10 . Now, consider a random sample of n = 50 NASCAR races and let x represent the sample mean time until the first critical part failure.

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 until the first critical part failure exceeds .13 hour.