In sports betting, 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 this 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. Suppose that in games, the margin of victory for the favored team relative to the spread is approximately normally distributed with a mean of −1.0 point and a standard deviation of 11.1 points. Complete parts (a) through (c) below. (a) What is the probability that the favored team wins by 7 or more points relative to the spread? The probability is nothing. (Round to four decimal places as needed.) (b) What is the probability that the favored team loses by 3 or more points relative to the spread? The probability is nothing. (Round to four decimal places as needed.) (c) In games where a team is favored by more than 12 points, what is the probability that the favored team "beats the spread"? Does this imply that the possible point shaving spreads are accurate for games in which a team is favored by more than 12 points? The probability is nothing. (Round to four decimal places as needed.) Does this imply that the possible point shaving spreads are accurate for games in which a team is favored by more than 12 points? A. The fact that the favored team is less likely to lose than to win relative to the spread means that the spreads are not accurate. There is possible point shaving. B. The fact that the favored team is just as likely to lose as they are to win relative to the spread means that the spreads are accurate. There is no evidence of point shaving. C. The fact that the favored team is just as likely to lose as they are to win relative to the spread means that the spreads are not accurate. There is possible point shaving. D. The fact that the favored team is more likely to lose than to win relative to the spread means that the spreads are not accurate. There is possible point shaving
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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