# Question: In sports betting Las Vegas sports books establish winning margins

In sports betting, Las Vegas sports books establish winning margins for a team that is favored to win a game. An individual can place a wager on the game and will win if the team bet upon wins after accounting for the spread. For example, if Team A is favored by 5 points, and wins the game by 7 points, then a bet on Team A is a winning bet.

However, if Team A wins the game by only 3 points, then a bet on Team A is a losing bet. In games where a team is favored by 12 or fewer points, the margin of victory for the favored team relative to the spread is approximately normally distributed with a mean of 0 points and a standard deviation of 10.9 points.

(a) In games where a team is favored by 12 or fewer points, what is the probability that the favored team wins by 5 or more points relative to the spread?

(b) In games where a team is favored by 12 or fewer points, what is the probability that the favored team loses by 2 or more points relative to the spread?

(c) Explain the meaning of “the margin of victory relative to the spread has a mean of 0 points.” Does this imply that the spreads are accurate for games in which a team is favored by 12 or fewer points?

However, if Team A wins the game by only 3 points, then a bet on Team A is a losing bet. In games where a team is favored by 12 or fewer points, the margin of victory for the favored team relative to the spread is approximately normally distributed with a mean of 0 points and a standard deviation of 10.9 points.

(a) In games where a team is favored by 12 or fewer points, what is the probability that the favored team wins by 5 or more points relative to the spread?

(b) In games where a team is favored by 12 or fewer points, what is the probability that the favored team loses by 2 or more points relative to the spread?

(c) Explain the meaning of “the margin of victory relative to the spread has a mean of 0 points.” Does this imply that the spreads are accurate for games in which a team is favored by 12 or fewer points?

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