A manufacturer knows that their items have a normally distributed lifetime, with a mean of 10 years, and standard deviation of 3 years and one of the piece is 11 years. There are three situation. The piece can die between now and age 13 which cost is maximum. Replacement at age 13 costs smaller than if we change immediately. what is the probability that the equipment will last up to 13 if not replaced now?
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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