An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with mean=117cm and standard deviation =5.2 cm. i) Find the probability that one selected subcomponent is longer than 120cm. ii) Find the probability that if four subcomponents are randomly selected, their mean length exceeds 120cm.
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!
An automatic machine in a manufacturing process is operating properly if the lengths
of an important subcomponent are
deviation =5.2 cm.
i) Find the probability that one selected subcomponent is longer than 120cm.
ii) Find the probability that if four subcomponents are randomly selected, their mean
length exceeds 120cm.
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