All Questions

Sumo Wrestlers

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Parts

Part 1

Two Sumo wrestlers (A and B) have one wrestling match each day for $N$ days. Let $X_i$ denote the outcome of a wrestling match on day $i$ for A (0 if A lost and 1 if A won) and let $\bar{X}_n$ denote the fraction of matches that A won.

Assume that each match is independent of the other matches and let $p$ denote the probability that sumo A wins the match. If $p = 0.63$, and $\sigma = 0.025$ how many matches must the sumo wrestlers have in order for $P(0.57 \leq \bar{X}_n \leq 0.69) \gt 0.88$.