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 negative 1.0 point and a standard deviation of 11 points. Complete parts (a) through (c) below. (a) What is the probability that the favored team wins by 6 or more points relative to the spread?

Answer 1

From the given data,

Here,

Mean, μ = -1.0

Standard deviation, σ = 11

(a) The probability that the favored team wins by 6 or more points relative to the spread

= P(X ≥ 6)

= P[Z ≥ {6 - (-1)}/11]

= P{Z ≥ 7/11}

= P(Z ≥ 0.6364)

= 0.2623