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Q31Section A (Section A)31 of 35

Sample size from Chebyshev's inequality for a proportion of heads

Let SnS_n denote the number of heads obtained in nn independent tosses of a fair coin. Using Chebyshev's inequality, the smallest values of nn such that

P(∣Snn−12∣≤0.1)≥34,P\left(\left|\frac{S_n}n-\frac12\right|\le0.1\right)\ge\frac34,

is

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