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; othenNise you lose $1. Complete parts (a) through (9) below. f ..... '\\ \\/ (a) Construct a probability distribution for the random variable X, the winnings of each spin. x P(x) 35 0.0263 - 1 0.9737 (Type integers or decimals rounded to four decimal places as needed.) (b) Determine the mean and standard deviation of the random variable X. Round your results to the nearest penny. p.= -0.05 cr= 5.76 (c) Suppose that you play the game 70 times so that n =70. Describe the sampling distribution of i, the mean amount won per game. The sample mean )_( is approximately normal. What are the mean and standard deviation of the sampling distribution of )_(? Round your results to the nearest penny. "i = - 0.05 o; = 0.69 (d) What is the probability of being ahead after playing the game 70 times? That is, what is the probability that the sample mean is greater than 0 for n = 70? Pp} > 0) = 0.4721 (Type an integer or decimal rounded to four decimal places as needed.) (1) Compare the results of parts (d) through (f). What lesson does this teach you? O A. The probability of being ahead decreases as the number of games played decreases. O B. The probability of being ahead decreases as the number of games played increases. 0 C. The probability of being ahead increases as the number of games played increases. 0 D. The probability of being ahead remains the same as the number of games played varies. (d) What is the probability of being ahead after playing the game 70 times? That is, what is the probability that the sample mean is greater than 0 for n = 70? P0} > 0) = 0.4721 (Type an integer or decimal rounded to four decimal places as needed.) (9) What is the probability of being ahead after playing the game 140 times? Po} > 0) = 0.4591 (Type an integer or decimal rounded to four decimal places as needed.) (f) What is the probability of being ahead after playing the game 700 times? Po} > 0) = 0.4045 (Type an integer or decimal rounded to four decimal places as needed.)