1. A friend has offered to play a gambling game with you that involves flipping a coin that be 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 heads is actually 0.50, as it should be if the coin is fair. (a) Assume for the moment that the coin is fair. If its is the proportion of heads in 50 flips of the coin, what are the mean and standard deviation of the sampling distribution oft?

2. Explain why you can use the formula for the standard deviation of pin this setting.

3. You flip the coin SO 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.