The mean cost to Metropolis of an insured hospitalized influenza patient is $5634 with a standard deviation of $1204 mg. Let us assume that the cost for any patient is independent from the cost of any other patient. In the coming influenza season, Metropolis expects 28900 insured hospitalized influenza patients. Suppose we look at the cost of each hospitalized influenza patient during the influenza season. Let M be the random variable representing the mean cost of all the 28900 insured hospitalized influenza patients. Let T = the random variable representing the total cost of the 28900 insured hospitalized influenza patients. a) What theorem will let us treat T and M as approximately normal random variables? Law of Large Numbers Convolution Theorem Chebychev's Theorem 301 Theorem Monte Carlo Theorem Central Limit Theorem b) What is the expected value of T? c) What is the standard deviation of T?

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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!