Critical part failures in NASCAR vehicles. The Sport Journal (Winter 2007) published an analysis of critical part failures at NASCAR races. The researchers found that the time y (in hours) until the first critical part failure has a highly skewed distribution with μ = .10 and σ = .10. Now, consider a random sample of n = 50 NASCAR races and let y¯ represent the sample mean time until the first critical part failure.
(a) Find E(y¯) and Var(y¯).
(b) Although y has a highly skewed distribution, the sampling distribution of y¯ is approximately normal. Why?
(c) Find the probability that the sample mean time until the first critical part failure exceeds .13 hour.