Inflippingabalancedcoin n times, areyoumorelikelytohave(i)between40and60heads in 100flips,or(ii)between490and510headsin1000flips?As n increases, explainwhythe proportion of headsconvergestoward1/2(becausethestandarderrorofasample proportion decreases) butthe number of

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Inflippingabalancedcoin n times, areyoumorelikelytohave(i)between40and60heads in 100flips,or(ii)between490and510headsin1000flips?As n increases, explainwhythe proportion of headsconvergestoward1/2(becausethestandarderrorofasample proportion decreases) butthe number of headsneednotbecloseto n~2 (becausethestandarddeviation of abinomial number of successesincreases).

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