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. Researchers conducted a study of critical-part failures from 36 NASCAR races. The researchers discovered that the time (in hours) until the first critical-part failure is exponentially distributed with a mean of 0.10 hour. Consider a random sample of n -50 NASCAR races and let x-bar represent the sample mean time until the first critical part failure.

a.) What is the mean of the sampling distribution of sample mean?
b.) What is the standard error of the mean?
c.) What is the probability that the sample mean time until the first critical part failure exceeds 0.13 hour?