(a) If a team is selected at random, find the probability the team scored at least 31 touchdowns. 0.698 (Round to three decimal places as needed.) (b) If a team is selected at random, find the probability the team scored between 40 and 48 touchdowns inclusive. (Round to three decimal places as needed.)

To solve the problem, we need to find the probabilities based on the given conditions. However, we need more information about the distribution of touchdowns scored by the teams, such as the total number of teams, the mean, and the standard deviation if it's a normal distribution, or the specific counts of teams scoring certain touchdowns. Let's assume we have the following known conditions: 1. The total number of teams (N). 2. The number of teams that scored at least 31 touchdowns (A). 3. The number of teams that scored between 40 and 48 touchdowns inclusive (B). ### (a) Probability of scoring at least 31 touchdowns The probability \( P(A) \) can be calculated using the formula: \[ P(A) = \frac{A}{N} \] Where: - \( A \) is the number of teams that scored at least 31 touchdowns. - \( N \) is the total number of teams. Given that \( P(A) = 0.698 \), we can conclude that the probability of selecting a team that scored at least 31 touchdowns is already provided. ### (b) Probability of scoring between 40 and 48 touchdowns inclusive The probability \( P(B) \) can be calculated using the formula: \[ P(B) = \frac{B}{N} \] Where: - \( B \) is the number of teams that scored between 40 and 48 touchdowns inclusive. To find \( P(B) \), we need the value of \( B \) and the total number of teams \( N \). If we assume we have this data, we can calculate the probability. If you provide the values for \( B \) and \( N \), I can calculate the probability for part (b).