scored 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.)

In statistical analysis, understanding the distribution of scores can lead to intriguing insights about performance. When considering probabilities related to scores, it’s common to use normal distributions or binomial distributions, depending on the nature of the data. In your question, if 31 touchdowns are a cutoff, referencing historical data on team scores like average touchdowns per season can aid in establishing context and making informed predictions. For your second point, let’s say you want to find the probability of scoring between 40 and 48 touchdowns. To accurately calculate that, you'll need either a set of data showing how many teams scored within that range or a probability distribution function (pdf). Once you have the distribution, you can integrate over that range or simply look at the probabilities listed in a cumulative distribution table to provide the probabilities for a more accurate outcome.