Question

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

point and a standard deviation of 11.4 points.

​(b) What is the probability that the favored team loses by 22 or more points relative to the​ spread?

Answer 1

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 an will win if the team bet upon wins after accounting for this spread .

Team A is favored by 5 points , and wins the game by only 3 points, then a betting on team A is a losing bet.

The margin of victory for the favored team relative to the spread is approximately normally distributed with a mean of -1.

And standard deviation of 11.4 points.

P( X < A) = P( Z <

mean = -1

standard deviation = 11.4 points

b) The probability that the favored team loses by 22 or more points relative to the spread.

P( X 22) = 1 - P(X 22)

= 1 -

= 1 - p(

= 1 - p(Z < 1.9298)

= 1 - 0.9732

= 0.0268

P( X 22 ) = 0.0268