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Fuel Consumption and Cars

The purpose of an automobile's 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 mean 100,000 miles.

a. Find the value of λ.

b. Find the probability that a randomly selected timing belt lasts for more than 120,000 miles.

c. Find the probability that a randomly selected timing belt lasts for between 75,000 and 125,000 miles.

d. If the timing belt on a new car breaks within 70,000 miles, the dealer will install a new belt free of charge. What is the probability the dealer will be forced to install a new timing belt free of charge on a randomly selected car?

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