method. After a training period, the average time these 9 employees take to perform thesametask is 13.5 minutes. The plant manager would like to be at least 98% sure before switching any more employees to the new, perhaps faster method and
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!
The mean length of time required to perform a certain assembly line task at Joe’sManufacturinghas been established to be 15.5 minutes, with a standard deviation of 3 minutes. A random sample of 9 employees aretaught a new method. After a training period, the average time these 9 employees take to perform thesametask is 13.5 minutes. The plant manager would like to be at least 98% sure before switching any more employees to the new, perhaps faster method and consults you for advice. Do these results provide sufficient evidence to indicate that the new method is fasterthan the old? Use the critical value approachto develop and test appropriate hypotheses concerning this situation. What would you advise the manager under these circumstances?
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