The Chemco Company manufactures car tires that last distances that are normally distributed with a mean of 57,300 km and a standard deviation of 6875 km.
a. If a tire is randomly selected, what is the probability that it lasts more than 48,000 km?
b. If 40 tires are randomly selected, what is the probability that they last distances that have a mean greater than 56,300 km?
c. If the manufacturer wants to guarantee the tires so that only 3% will be replaced because of failure before the guaranteed number of kilometres, for how many kilometres should the tires be guaranteed?