Refer to The Sport Journal (Winter 2007) analysis of critical part failures at NASCAR races, Exercise 5.106 (p. 271). Recall that researchers found that the time x (in hours) until the first critical part failure is exponentially distributed with µ = .10 and σ = .10. Now, consider a random sample of n = 50 NASCAR races and let x̅ represent the sample mean time until the first critical part failure.

a. Find E (x̅) and Var (x̅).

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

c. Find the probability that the sample mean time until the first critical part failure exceeds .13 hour.