A bag contains an unknown number of red and black marbles, but you do know that there are more black marbles than red. You are allowed to make a number of draws from the bag (w/ replacement) and if you draw at least as many red marbles as black you win the jackpot of $100. a. Would you rather make 50 draws from the bag or 200 draws, or does it not matter? Justify your answer. (Hint: Draw a picture of the sampling distribution) b. If the game is changed so that you win if you draw at least as many black marbles as red how does this change your answer? We've been studying the central limit theorem and sampling distributions, but I don't understand how I am supposed to figure this out without knowing the population or the standard deviation. Obviously, the larger the sample will be better, but I don't understand how I am supposed to prove it.
A bag contains an unknown number of red and black marbles, but you do know that there are more black marbles than red. You are allowed to make a number of draws from the bag (w/ replacement) and if you draw at least as many red marbles as black you win the jackpot of $100.
a. Would you rather make 50 draws from the bag or 200 draws, or does it not matter? Justify your answer. (Hint: Draw a picture of the sampling distribution)
b. If the game is changed so that you win if you draw at least as many black marbles as red how does this change your answer?
We've been studying the central limit theorem and sampling distributions, but I don't understand how I am supposed to figure this out without knowing the population or the standard deviation. Obviously, the larger the sample will be better, but I don't understand how I am supposed to prove it.
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