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 0 points and a standard deviation of 11.8 points. Complete parts a through c below.

a) What is the probability that the favored team wins by 9 or more points relative to the​ spread?

Answer 1

The probability that the favored team wins by 9 or more points relative to the spread is approximately 77.64%.

Step-by-step explanation:

To find the probability that the favored team wins by 9 or more points relative to the spread, we need to calculate the probability of the margin of victory being greater than or equal to 9 points using the given normal distribution.

We can convert this problem into a standardized normal distribution problem using the formula:
Z = (X - μ) / σ

Where:
X = 9 (the margin of victory we want to find the probability for)
μ = 0 (mean of the distribution)
σ = 11.8 (standard deviation of the distribution)

By substituting these values into the formula, we get:
Z = (9 - 0) / 11.8 = 0.76

We can now look up the probability corresponding to a z-score of 0.76 on the standard normal distribution table or use a calculator to find that the probability is approximately 0.7764, or 77.64%.