In the game of roulette, a wheel consists of 38 slots numbered 0, 00, 1, 2, . . . , 36. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. If the number of the slot the ball falls into matches the number you selected, you win $35; otherwise you lose $1.

(a) Construct a probability distribution for the random variable X, the winnings of each spin.
(b) Determine the mean and standard deviation of the random variable X. Round your results to the nearest penny.
(c) Suppose that you play the game 100 times so that n = 100. Describe the sampling distribution of x̄, the mean amount won per game.
(d) What is the probability of being ahead after playing the game 100 times? That is, what is the probability that the sample mean is greater than 0 for n = 100?
(e) What is the probability of being ahead after playing the game 200 times?
(f ) What is the probability of being ahead after playing the game 1000 times?
(g) Compare the results of parts (d) and (e). What lesson does this teach you?

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