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Critical part failures in NASCAR vehicles. Refer to The Sport Journal (Winter, 2007) analysis of critical part failures at NASCAR races, Exercise 5.102 (p. 260). 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 represent the sample mean time until the first critical part failure.
a. Find E() and Var().
b. Although x has an exponential distribution, the sampling distribution of is approximately normal. Why?
c. Find the probability that the sample mean time until the first critical part failure exceeds .13 hour.
Exercise 5.102
Critical-part failures in NASCAR vehicles. In NASCAR races such as the Daytona 500, 43 drivers start the race; however, about 10% of the cars do not finish due to the failure of critical parts. University of Portland professors conducted a study of critical-part failures from 36 NASCAR races (The Sport Journal, Winter 2007). The researchers discovered that the time (in hours) until the first critical-part failure is exponentially distributed with a mean of .10 hour.
a. Find the probability that the time until the first critical part failure is 1 hour or more.
b. Find the probability that the time until the first critical part failure is less than 30 minutes.
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