Answer :
Sam and Hector will weigh the same after 10 weeks, both reaching 225 pounds. The California quarterback was approximately 0.79 standard deviations below the mean weight of a Texas football player. The California quarterback was lighter compared to the Texas player.
To find out when Sam and Hector will weigh the same amount, we set up an equation based on their current weights and weekly weight gain. Sam starts at 205 pounds and gains 2 pounds per week, while Hector starts at 195 pounds and gains 3 pounds per week. We are looking for the number of weeks where their weights will be equal.
Let w represent the number of weeks. For Sam: 205 + 2w, and for Hector: 195 + 3w. Setting these two expressions equal to each other gives us the equation:
205 + 2w = 195 + 3wSolving for w, we subtract 2w from both sides, and we also subtract 195 from both sides:
205 - 195 = 3w - 2w10 = w
Therefore, Sam and Hector will weigh the same after 10 weeks.
To find out how much they will weigh at that time, we simply substitute w back into one of the original equations:
Sam's weight after 10 weeks: 205 + 2(10) = 225 poundsSo, in 10 weeks, they will both weigh 225 pounds.
Now, regarding the quarterback's weight compared to the mean, first we calculate the z-score for the quarterback's weight:
Z = (individual's weight - mean weight) / standard deviationZ = (205 - 240.08) / 44.38
Z ≈ -0.79
This means that the quarterback was about 0.79 standard deviations below the mean weight for a player from the Texas football team.
Comparing the California quarterback and the Texas player, we observe that the California quarterback weighed 205 pounds and the Texas player weighed 209 pounds. Since both weights were below the team's mean of 240.08 pounds, to determine who was lighter, we simply compare their weights directly. The California quarterback was lighter because he weighed less than the Texas player.
