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The Bureau of Labor Statistics reports the fatality rate for

The Bureau of Labor Statistics reports the fatality rate for workers in the rail transportation industry is 0.006 fatalities per 200,000 worker-hours. During 2007, rail transportation workers put in a total of 545 million worker-hours. Assuming that (1) an exponential distribution applies for the number of worker-hours between fatalities in this industry, and (2) the annual 545 million worker-hours of activity continues in the industry, what is the expected number of worker-hours until the next fatality occurs in this industry? If a given rail transportation company requires 1,000,000 worker-hours each year, what is the probability that the next fatal injury in this company will not occur until at least 30 years from now?

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