The average number of miles (in thousands) that a car's tire will function before needing replacement is 72 and the standard deviation is 12. Suppose that 41 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of xx? xx ~ N(,)
3. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 72.8 and 75.4.
4. For the 41 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 72.8 and 75.4.
5. For part d), is the assumption that the distribution is normal necessary? NoYes