One thousand coins were each flipped eight times, and the number of heads were recorded for each coin. The results are as follows: Number of heads Number of coins 0 6 1 32 2 105 3 186 4 236 5 201 6 98 7 33 8 103 A: Test whether the distribution of coin flips matches the expected frequencies from a binomial distribution asumming all fair coins (A coin is fair if the probability of heads per flip is 0.5).  B: If the binomal distribution is a poor fit to the data, identify in what way the distribution does not match the expectation.  C: Some two-headed coins (which always show heads on every flip) were mixed in with the fair coins. Can you say approximately how many two-headed coins there might have been out of this 1000?

Question

One thousand coins were each flipped eight times, and the number of heads were recorded for each coin. The results are as follows:

Number of heads Number of coins
0 6
1 32
2 105
3 186
4 236
5 201
6 98
7 33
8 103

A: Test whether the distribution of coin flips matches the expected frequencies from a binomial distribution asumming all fair coins (A coin is fair if the probability of heads per flip is 0.5). 

B: If the binomal distribution is a poor fit to the data, identify in what way the distribution does not match the expectation. 

C: Some two-headed coins (which always show heads on every flip) were mixed in with the fair coins. Can you say approximately how many two-headed coins there might have been out of this 1000?

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