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Rolling A Fair Eight Sided Die Produces A Uniformly Distributed Set Of Numbers Between 1 And 8 With A Mean Of 4.5 And A Standard Deviation Of 2.291. Assume That N Eight-sided Dice Are Rolled Many Times And The Mean Of The N Outcomes Is Computed Each Time. Find The Mean And Standard Deviation Of The Resulting Distribution Of Sample Means For N=36 - Math Discussion

Rolling a fair eight sided die produces a uniformly distributed set of numbers between 1 and 8 with a mean of 4.5 and a standard deviation of 2.291. Assume that n eight-sided dice are rolled many times and the mean of the n outcomes is computed each time. Find the mean and standard deviation of the resulting distribution of sample means for n=36