Final answer:
To determine who was lighter relative to their team's weight distribution, the California quarterback's or the Texas player's z-scores must be calculated and compared. This requires the team's mean and standard deviation, which are only provided for the Texas team in our example. Without the California team's statistics, a definitive comparison is not possible.
Step-by-step explanation:
The question revolves around statistics, specifically the use of mean and standard deviation to compare the weights of players on different football teams.
When comparing the famous quarterback from California who weighed 205 pounds to the player from the Texas football team who weighed 209 pounds, we need to determine who was lighter in comparison to their respective team averages.
To do this, we calculate the number of standard deviations from the mean for each player. The California quarterback's weight in standard deviations from the mean can be found if the mean and standard deviation for his team are known.
As for the player from the Texas team, whose team average is 240.08 pounds with a standard deviation of 44.38 pounds, we can calculate his z-score by subtracting the mean from his weight and dividing by the standard deviation.
This can be equated as (209 - 240.08) / 44.38 = -0.70 approximately. This shows that the Texas player is 0.70 standard deviations below his team's mean.
To conclude who is lighter relative to their team, we would compare the absolute value of the z-scores of each player, with the lower value indicating a weight closer to the team average. However, the California quarterback's z-score calculation requires his team's mean and standard deviation which have not been provided.