4) A tire manufacturer claims that the useful life of its tire is

normally distributed with M = 35,000 miles and C= 5,000 miles

a) If one tire is selected at random, What is the probability that

it lasts less than 31,000 miles?

b) If a consumer agency finds that one tire lasts less than

31,000 miles, would that be unusual? Do you think they

should doubt the manufacturer's claim? [ Explain using your

answer from part (a),

c) If a sample of 90 tires is considered, what is the probability

that their mean life, X, is less than 31,000 miles?

d) If a consumer agency tests 90 tires and finds that the mean

life is less than 31,000 miles, would that be unusual?

Do you think they should doubt the manufacturer's claim?

[Explain using your answer from part (C)).

e) What is the main idea of the Central Limit Theorem? (don't just quote the theorem.)

f) what do the symbols MX and Tx represent ?