The average number of miles (in thousands) that a car's tire will function before needing replacement is 64 and the standard deviation is 14. Suppose that 49 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 ? ~ N(,)
2. What is the distribution of ? ~ 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 61.4 and 63.
4. For the 49 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 61.4 and 63.
5. For part d), is the assumption that the distribution is normal necessary? NoYes