Question: Is this coin balanced? While he was a prisoner of war during World War II, John Kerrich tossed a coin 10,000 times. He got 5067 heads. If the coin is perfectly balanced, the probability of a head is 0.5.

(a) Find the mean and the standard deviation of the number of heads in 10,000 tosses, assuming the coin is perfectly balanced.

(b) Explain why the Normal approximation is appropriate for calculating probabilities involving the number of heads in 10,000 tosses.

(c) Is there reason to think that Kerrich's coin was not balanced? To answer this question, use a Normal distribution to estimate the probability that tossing a balanced coin 10,000 times would give a count of heads at least this far from 5000 (that is, at least 5067 heads or at most 4933 heads).