During 2008, U.S. general aviation pilots had 1.20 fatal crashes per 100,000 flying hours. Harriet Arnold is president of Arnold’s Flying Service, a company that operates a total of 50 sightseeing planes based in 20 regions of the United States. Altogether, the planes in this fleet are in the air about 40,000 hours per year. Ever since a fatal crash last year involving one of the company’s planes that took off under questionable weather conditions, the company has been getting close scrutiny from both government safety officials and the national media. Harriet believes her planes are just as safe as anyone else’s, but is concerned that even one more fatal accident within the coming year might be too much for the now-struggling company to overcome. Assuming an exponential distribution for x = thousands of flying hours between fatal crashes, what is the probability that Arnold’s Flying Service will not experience a fatal crash until at least a year from today? Until at least 2 years from today? What number of flying hours would be associated with a 90% probability of experiencing no crashes within that number of flying hours from today?
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