Suppose that Dunlop Tire manufactures a tire with a lifetime that approximately follows a normal distribution with mean 70,000 miles and standard deviation 4400 miles.
(a) What proportion of the tires will last at least 75,000 miles?
(b) Suppose that Dunlop warrants the tires for 60,000 miles. What proportion of the tires will last 60,000 miles or less?
(c) What is the probability that a randomly selected Dunlop tire lasts between 65,000 and 80,000 miles?
(d) Suppose that Dunlop wants to warrant no more than 2% of its tires. What mileage should the company advertise as its warranty mileage?