The purpose of an automobile timing belt is to provide a connection between the camshaft and the crankshaft. This allows the valves to open and close in sync with the pistons. Suppose the duration of a timing belt (in miles) can be modeled by an exponential random variable with parameter ?? = 0.00002.
What are the expected value and variance of the duration of a timing belt?
What is the probability that a randomly selected timing belt lasts for more than 60,000 miles?
If the timing belt on a new car breaks within 20,000 miles, the dealer will install a new belt free of charge. What is the probability that the dealer will be forced to install a new timing belt free of charge on a randomly selected car?
What is the 80th percentile of the duration of timing belts?