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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