(31) A baseball teams plays 182 games in a season and we are tracking their record over three seasons. Assume the probability the team wins each game in Season 1, Season 2, and Season 3 is 0.45, 0.6, and 0.4, respectively. Let X be the total number of games the team wins over the three seasons. (a) Use Poisson approximations to binomial distributions to estimate P(X = 260). (b) Use normal approximations to binomial distributions to estimate P(X > 270).

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