A company that manufactures mufflers for cars offers a lifetime warranty on its products provided that ownership of the car does not change. Suppose that only 20% of its mufflers are replaced under this warranty.

a. Define the random variable X as the number of mufflers replaced in a sample of 400 purchases. Give the distribution of X.

b. Referring to part 2a), what is the approximate probability that between 75 and 100 mufflers (inclusive) arc replaced under warranty?

c. Among 400 randomly selected purchases, what is the approximate probability that at most 70 are ultimately replaced under warranty?