The Boston Celtics play 52 games against their 14 Eastern Conference rivals each

Question

The Boston Celtics play 52 games against their 14 Eastern Conference rivals each regular season. They play 20 vs. teams in the North division, 16 vs. teams in the South division, and 16 vs. teams in the Midwest division. Suppose the probability they win vs. a team in the North is 0.8, the probability they win vs. a team in the South is 0.7, and the probability they win vs. a team in the midwest is 0.6. Assuming the outcomes of games are independent of each other and using the normal approximation to the binomial, find the probability they win 40 or more of the 52 games.

Explanation / Answer

mean = 36.8

Hence probability of winning, p = 36.8/52 = 0.7077

mean = np = 36.8

std.dev. = sqrt(npq) = sqrt(52 * 0.7077 * (1-0.7077)) = 3.2798

P(X > 40) = P(z > (40 - 36.8)/3.2798) = P(z > 0.9757) = 0.1646

Required probability = 0.1646

No. of games(f) P(x) f*P(x) North 20 0.8 16 South 16 0.7 11.2 Midwest 16 0.6 9.6 52 36.8

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