3. Sampling Distribution of p: You plan to spend Saturday night at the casino be

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3. Sampling Distribution of p: You plan to spend Saturday night at the casino betting on dice. In the casino game of Craps, a pair of fair dice is tossed and the sum of the two individual dice is recorded. If a 7 or an 11 appears on the first roll of the dice, then the Roller wins the game. Suppose the outcome of your bet depends only on the first roll, in which you win $3 if a 7 or 11 appears and lose $1 if a 7 or 11 does not appear a. You plan to stay at the casino for 150 rounds of betting. Sketch the sampling distribution of the proportion of games you will win (p). b. What is the probability that you will have a profitable evening? c. What is the probability that you will lose money overall, but your losses will be less than $25? d. Using the statistical software R, simulate 500 iterations of your evening at the casino. Produce a histogram of the proportion of 150 games won for the simulated evenings. Produce a histogram of the net winnings for the simulated evenings. Are your results consistent with your answers in (a)Hc)? 4. Central Limit Theorem: Suppose that you own a casino and you are considering the installation of two different slot machines. Both slot machines accept $1 bets with payouts and win probabilities given below Slot Machine A Slot Machine B Win $10 Lose $1 Probability 0.0818Win $10,000 Probability 0.9182 Probability 0.00009 Probability 0.99991 Lose $1 In the long run, how much can a player expect to lose per game playing i) Slot Machine A and il) Slot Machine B? Suppose that in one evening, a total of 1,000 bets are placed on Slot Machine A. Compute the probability that the casino loses money that evening. a. b. Suppose that in one evening, a total of 1,000 bets are placed on Slot Machine B. Compute the probability that the casino loses money that evening. Hint: Use Binomial Probability (not CLT Compute the minimum number of total bets that must be placed per evening on Slot Machine A so that the casino can be 99% certain that it will not lose money each evening. Compute the minimum number of total bets that must be placed per evening on Slot Machine B so that the casino can be 99% certain that it will not lose money each c. d. e. evening.

Explanation / Answer

3. answer is A the sampling distribution of p

the plan of the die canbe stay  

because 7 is only winner of the first roll you are roll 7 while try getting to a point and you lose

roll a pair of dice and the sum of 2 individual dice getting 7 or 11

also the 2,3,4,11 only special for the first roll if roll 2, 3, 4,11 while trying to get a point you ignore it

only the point 7 get a pont and win the game

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