private consumption as a share of GDP is a random quantity that follows a roughly normal distribution. according to an article in business week, for the united state that was about 71%. assuming that this value is the mean of a normal distribution and that the standard deviation of the distribution is 3%, what is the value of private consumption as a share of GDP such that you are 90% sure that the actual value falls below it?
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!
private consumption as a share of GDP is a random quantity that follows a roughly
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