NCAA Basketball Point Spreads 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 Showing: 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?
NCAA Basketball Point Spreads 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 Showing: 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?
NCAA Basketball Point Spreads 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 Showing: 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?
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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