12. A friend has offered to play a gambling game with you that involves flipping

Question

12. A friend has offered to play a gambling game with you that involves flipping a coin that he has provided. Since a flip of heads will be to his advantage, you want to test the coin for fairness before you begin to play. Your friend is willing to let you flip the coin 50 times to determine if the probability of getting headsis actually 0.50, as it should be if the coin is fair. (a) Assume for the moment that the coin is fair. If bis the proportion ofheads in 50 flips of the coin, what are the mean and standard deviation ofthe sampling distribution of A? (b) Explain why you can use the formula for the standard deviation of p in this setting. (c) You flip the coin 50 times and get 30 heads. Do you risk insulting your friend by refusing to play with his coin? Support your answer with an appropriate probability calculation.

Explanation / Answer

1)mean for a fair coin is always 0.5 st d= 0.5-(.5)^2 =0.25 2)because this is the standard standard deviation formula 3)definitely not, because probability of a coin heads or tails are the same for any coin that is 1/2=0.5

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