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. Source: Justin Wolfers, "Point Shaving: Corruption in NCAA Basketball"
(a) 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?
(b)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?
(c)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?