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) 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 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 b) rounded to 4 decimal places. You must show all of your steps
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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