A roulette wheel in a casino has 38 slots. If you bet a dollar on a particular number, you'll win $32 if the ball ends up in that slot and $0 otherwise. Roulette wheels are calibrated so that each outcome is equally likely. Complete parts (a) through(c).a. Let X denote your winnings when you play once. State the probability distribution of X. (This also represents the population distribution you would get if you could play roulette an infinite number of times.) It has mean 0.842 and standard deviation 5.122 X Probability 0 0.973684 32 0.026316 (Round to six decimal places as needed.) b. You decide to play once a minute for a total of 1050 times. Find the mean and standard deviation of the sampling distribution of your sample mean winnings The mean is 0.842 (Round to the nearest thousandth as needed.) The standard deviation is 0.158 (Round to the nearest thousandth as needed.) c. Refer to (b). Using the central limit theorem, find the probability that with this amount of roulette playing, your mean winnings is at least $1, so that you have not lost money. (Hint: Find the probability that a normal random variable with mean equal to the mean from part b and standard deviation equal to the standard deviation from part b exceeds 1.0.) The probability is (Round to the nearest hundredth as needed.)
