Consider the following simple game of chance. You flip a fair coin. If the result is heads, you win $100, but if the result is tails, you lose $101. Let A be your random "winnings" on one play of the game. That is, if you get a head, then A=100, but if you get a tail, then A=-101. It can be shown that the mean of A is –0.5 and the standard deviation are 100.5. Let an be your cumulative "winnings" on n plays of the game. Which of the following is true when n=100?

a. The sampling distribution of An has mean -5 and standard deviation 1,005.

b. The sampling distribution of An has mean -50 and standard deviation 10,050.

c. The sampling distribution of An has mean -5 and standard deviation 10,050.

d. The sampling distribution of An has mean -50 and standard deviation 1,005.

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