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5. Reliability studies use an exponential probability distribution to express the expected life time of a piece of machinery. A packaging machine in a factory has an expected lifetime of 20 years. a) (3 points) Determine the cumulative distribution function for this piece of machinery. You must show all of your steps or explain how you got to your answer to receive full credit. b) (5 points) Find the probability that a machine which is 18 years old will last at least another 10 years before it breaks down. Give both an exact value numeric answer and an approximation rounded to 4 decimal places. You must show all of your steps to receive full credit