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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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? [Text Box]

c) What is the standard deviation of T? [Text Box]

d) If TK is T/2000 then what is the standard deviation of TK? [Text Box]

e) What is the approximate probability that T is greater than $163,000,000? [Text Box]

f) What is the standard deviation of M? [Text Box]

g) What is the approximate probability M is between 5630 and 5700? [Text Box]

h) Metropolis will set up an influenza contingency fund, F, so that there is only a 10% chance that the total cost of the 28900 hospitalized influenza patients will be greater than F? What is the desired F? [Text Box]
Transcribed Image Text: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? [Text Box] c) What is the standard deviation of T? [Text Box] d) If TK is T/2000 then what is the standard deviation of TK? [Text Box] e) What is the approximate probability that T is greater than $163,000,000? [Text Box] f) What is the standard deviation of M? [Text Box] g) What is the approximate probability M is between 5630 and 5700? [Text Box] h) Metropolis will set up an influenza contingency fund, F, so that there is only a 10% chance that the total cost of the 28900 hospitalized influenza patients will be greater than F? What is the desired F? [Text Box]
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