A commuter train arrives punctually at a station every twenty-five minutes. Each morning, a commuter named Andrew leaves his house and casually strolls to the train station. Assume that the time he arrives at the station is random and uniform. Let X be the amount of time, in minutes, that Andrew waits for the train. (a) What kind of distribution is associated with the waiting time X? Give a graph to describe the shape of the distribution of X.
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!
A commuter train arrives punctually at a station every twenty-five minutes. Each
morning, a commuter named Andrew leaves his house and casually strolls to the train
station. Assume that the time he arrives at the station is random and uniform. Let X be
the amount of time, in minutes, that Andrew waits for the train.
(a) What kind of distribution is associated with the waiting time X? Give a graph to
describe the shape of the distribution of X.
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