Final answer:
Dak Prescott's quarterback rating for 2019 is 99.67. The famous quarterback from California is -0.79 standard deviations below the mean team weight. Comparatively, the player from Texas is -0.70 standard deviations below the mean, making the California quarterback lighter relative to his team.
Step-by-step explanation:
To calculate Dak Prescott’s quarterback rating for the 2019 season using the given formula, we will plug in his statistics: % completion (COMP), % touchdown (TD), % interception (INT), and yards per attempt (YD). The formula given is:
25 + 10(%COMP) + 40(%TD) - 50(%INT) + 50(YD) / 12
Substituting the values:
25 + 10(65.1) + 40(5) - 50(1.8) + 50(8.2) / 12
Calculation:
25 + 651 + 200 - 90 + 410 / 12
25 + 651 + 200 - 90 + 410 = 1196
1196 / 12 = 99.67
Therefore, Dak Prescott’s quarterback rating for the 2019 season is 99.67.
Next, to determine how many standard deviations above or below the mean weight the famous quarterback who weighed 205 pounds was, we use the formula:
(X - μ) / σ
Where X is the player’s weight, μ is the mean, and σ is the standard deviation. For the Texas team, μ = 240.08 and σ = 44.38.
(205 - 240.08) / 44.38
Calculation:
(-35.08) / 44.38 = -0.79
The famous quarterback is approximately -0.79 standard deviations below the mean.
To compare the California quarterback with the Texas player, we calculate the standard score (z-score) for the Texas player who weighed in at 209 pounds using the same formula:
(209 - 240.08) / 44.38
Calculation:
-31.08 / 44.38 = -0.70
The Texas player is approximately -0.70 standard deviations below the mean. Since -0.70 is closer to the mean than -0.79, the California quarterback was lighter compared to his team than the Texas player was to his team.