Manufacture of a certain component requires threedifferent machining operations. Machining time foreach operation has a normal distribution, and the threetimes are independent of one another. The mean valuesare 15, 30, and 20 min, respectively, and the standarddeviations are 1, 2, and 1.5 min, respectively. What isthe probability that it takes at most 1 hour of machiningtime to produce a randomly selected component?
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!
Manufacture of a certain component requires three
different machining operations. Machining time for
each operation has a
times are independent of one another. The mean values
are 15, 30, and 20 min, respectively, and the standard
deviations are 1, 2, and 1.5 min, respectively. What is
the probability that it takes at most 1 hour of machining
time to produce a randomly selected component?
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