Discuss the following:
Q: A Tire company has developed a new type of tire. Extensive testing shows that the number of miles the new tire will run before wearing out is normally distrubuted with a mean of 40,000 miles and a standard deviation of 4,000 miles (Hint: Sketch bell shaped curves for the three questions below.
a) What is the probability that the number of miles the new tire will run before wearing out is LESS than 33,000 miles?
b) What is the probability that the number of miles the tire will run before wearing out is between 42,500 and 44,500 miles?
c) The company wants to promote increased sales by offering a 10% discount on a new set of tires if the purchased set lasts longer than a specified number of miles. What mileage should the company set, if they want only 2% of the tires to exceed the specified mileage (i.e, 98% of the tires fail to exceed the specified mileage, with 2% in the right tail)?