Question: Problem 3: (10 pts) In the previous problem, you played a game where you had to roll 45 8-sided dice and won if you rolled

Problem 3: (10 pts) In the previous problem, you played a game where you had to roll 45 8-sided dice and won if you rolled a total of 180 or greater. a) Use a Monte Carlo method with N = 1000 trials to estimate the probability of victory. Include a .m (or .py) file with your submission containing your code, and report your estimate in the form of a 95 percent confidence interval u + 1.96s. b) Based on this result, about how many trials do you think you would have to run in order to get a standard error of 0.001 (that is, s = 0.001)? Justify your answer using the properties of the standard deviation (as opposed to using trial and error with your Monte Carlo code). Problem 3: (10 pts) In the previous problem, you played a game where you had to roll 45 8-sided dice and won if you rolled a total of 180 or greater. a) Use a Monte Carlo method with N = 1000 trials to estimate the probability of victory. Include a .m (or .py) file with your submission containing your code, and report your estimate in the form of a 95 percent confidence interval u + 1.96s. b) Based on this result, about how many trials do you think you would have to run in order to get a standard error of 0.001 (that is, s = 0.001)? Justify your answer using the properties of the standard deviation (as opposed to using trial and error with your Monte Carlo code)

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