(c) Give a careful and complete statement of the central limit theorem. Given a probability distribution of x values where n = sample size, μ = the mean of the x distribution, and σ = the standard deviation of the x distribution. Even if the x distribution is not normal, if the sample size n is sufficiently large ( n ? ≥ < 30 in most cases), the central limit theorem tells us that the x distribution is approximately ---Select--- geometric normal poisson binomial , the mean of the x distribution is μx = , and the standard deviation of the x distribution is σx = .
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!
(c) Give a careful and complete statement of the central limit theorem.
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