I've been stuck on this sample statistics problem for a couple days now:
Assume that two baseball teams have win records of $58\%$ and $54\%$. Demonstrate how to compute or estimate the number of games that must be played in order for the better team to win $70 \%$ of the time, $80\%$ of the time, and $90\%$ of the time.
I think the question is asking how many games must each team play against each other in order for the better team (team with the $0.58$ winning percentage) to win $X\%$ of the time. If I use a binomial distribution, the Central Limit Theorem and the $Z$ score formula I can work backwards and get a formula for the number of games. However, this approach only uses the winning percentage of the better team (i.e. $0.58$) which makes me think that I'm missing something important. Perhaps I'm misinterpreting the question?
Any thoughts or suggestions for how to approach this problem would be greatly appreciated!!!