Question

Is this coin balanced? While he was a prisoner of war during world war 2, John Kerrich tossed a coin 10,000 times. He counted how many times he got heads.

a. Is this setting binomial? Explain using the four characteristics of a binomial setting.

b. He got 5067 heads. if the coin is perfectly balanced, the probability of a head is 0.5. Is there reason to think that Kerrich’s coin was not balanced? To answer this question, find the probability that tossing a balanced coin 10,000 times would give a count of heads at least this far from 5,000 (that is, at least 5067 heads or no more than 4933 heads). Use a statistical software and post a picture of the output. If it is not binomial, then explain how the probability is computed.

Answer 1

a)

n = 10000, which is constant number of trils

p = 0.5, tossing a balanced coin

Coin outcomes are head or tail (only tow outcomes)

and probability remains constant at each trail

b)

P(X <= 4933 or X >= 5067)

Minitab > Data > Cal > Probability Distribution > Binomial

Output for P(X < 5067)

But we need P(X >= 5067) = 1-P(X < 5067) = 1-0.9115 = 0.0885

Output for P(X <= 4933) = 0.0918(Same as above)

P(X <= 4933 or X >= 5067) = 0.0885 + 0.0918 = 0.1803 = 18.03%

Coin is balanced because it is more than 5%