The average number of miles (in thousands) that a car's tire
will function before needing replacement is 70 and the standard
deviation is 10. Suppose that 46 randomly selected tires are
tested. Round all answers to 4 decimal places where possible and
assume a normal distribution.
- What is the distribution of X? X ~ N(__,__)
- What is the distribution of ¯x? x¯ ~ N(__,__ )
- 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 71.8 and 72.9.
- For the 46 tires tested, find the probability that the average
miles (in thousands) before need of replacement is between 71.8 and
72.9.
- For part d), is the assumption that the distribution is normal
necessary? Yes or No