Q6: A tire manufacturer states that a certain type of tire has a mean lifetime of 60,000 miles. Suppose lifetimes are no

[answerhappygod]

Q6: A tire manufacturer states that a certain type of tire has a
mean lifetime of 60,000 miles.
Suppose lifetimes are normally distributed with standard deviation
σ=3,500 miles. (10 marks)
a) Find the probability that if you buy one such tire, it will last
only 57,000 or fewer miles.
If you had this experience, is it particularly strong evidence that
the tire is not as good as
claimed?
b) A consumer group buys five such tires and tests them. Find the
probability that average
lifetime of the five tires will be 57,000 miles or less. If the
mean is so low, is that
particularly strong evidence that the tire is not as good as
claimed?