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Explain briey what the law of large numbers tells us about what will happen if the gambler makes a large number of bets on red. (c) The central limit theorem tells us the approximate distribution of the gamblers mean winnings in 50 bets. What is this distribution? Use the 689599.7 rule to give the range in which the mean winnings will fall 95% of the time. Multiply by 50 to get the middle 95% of the distribution of the gamblers winnings on nights when he places 50 bets. (d) What is the probability that the gambler will lose money if he makes 50 bets?

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