3.A SI bet on a single number on a casino's roul ette wheel pays \$35 ifthe ball ends up in the numberslot you choose. Here is the distribution of the payoff X:\$350.026Рayoff XProbability0.974Each spin of the roulette wheel is independent of other spinsWhat are the mean and standard deviation of X?a.Sam comes to the casino weekly and bets on 10 spins of the roul ette whel. What does the law oflarge numbers say about the average payoff Sam receives from his bets cach visiť?b.What does the central limit the or em say about the distribution of Sam's average payoff afterbetting on 520 spins in a year?c.Sam comes out ahead for the year if his average payoff is greater than \$1 (the amount he bets oneach spin). What is the probability that Sam ends the year ahead? The true probability is 0.396.Does using the central limit the orem provide a reasonable approximation?d.

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3d)

The probability that Sam ends the year ahead is 0.5079 and it is obtained below:

From the given information, Sam comes out head for the year if his average payoff is gr...

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