Assume you "tested" several Firestone tires and recorded their failure times (as defined by an engineer). After doing a Chi-Square test, you decide that failures are "normally" distributed, with mean failure of 50,000 miles and a standard deviation of 10,000 miles. Determine the following:
a. Reliability of the tires at 40,000 miles.
b. Given that a tire has been driven (on a test machine) 20,000 miles, determine its reliability at 60,000 miles.