Critical part failures in NASCAR vehicles. Refer to The Sport Journal (Winter 2007) analysis of critical part failures at NASCAR races, Exercise 5.106

(p. 299). Recall that 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 E1x2 and Var1x2.

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.