7. The purpose of an automobile's timing belt is to provide a connection between the camshaft...
7. 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 probability that a randomly selected timing belt lasts for more than 120,000 miles. (b) Find the probability that a randomly selected timing belt lasts for between 75,000 and 125,000 miles.