# Question

Use Chebyshev’s theorem and Theorem 5.3 to verify that the probability is at least 35 36 that

(a) In 900 flips of a balanced coin the proportion of heads will be between 0.40 and 0.60;

(b) In 10,000 flips of a balanced coin the proportion of heads will be between 0.47 and 0.53;

(c) In 1,000,000 flips of a balanced coin the proportion of heads will be between 0.497 and 0.503.

(a) In 900 flips of a balanced coin the proportion of heads will be between 0.40 and 0.60;

(b) In 10,000 flips of a balanced coin the proportion of heads will be between 0.47 and 0.53;

(c) In 1,000,000 flips of a balanced coin the proportion of heads will be between 0.497 and 0.503.

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