The relationship between a professional basketball player's height h in inches and weight w in pounds was modeled using two samples of players. The resulting modeling equations for the two samples were w equals 7.45 h minus 375 and w equals 7.92 h minus 406. Assume 65less than or equalshless than or equals85.
(a)
Use each equation to predict the weight of a professional basketball player who is 6 ' 8 ".
(b)
Determine graphically the height where the two models give the same weight.
(c)
For each model, what change in weight is associated with a 1-inch increase in height?
(a) To find the weight of a professional basketball player who is 6'8" using the first equation, we substitute h = 6*12 + 8 = 80 into the equation:
w = 7.45h - 375
w = 7.45(80) - 375
w = 596 - 375
w = 221 pounds
To find the weight using the second equation, we substitute h = 80 into the equation:
w = 7.92h - 406
w = 7.92(80) - 406
w = 633.6 - 406
w = 227.6 pounds
Therefore, the predicted weight of a professional basketball player who is 6'8" using the first equation is 221 pounds and using the second equation is 227.6 pounds.
(b) To find the height where the two models give the same weight, we set the two equations equal to each other:
7.45h - 375 = 7.92h - 406
This simplifies to:
0.47h = 31
h = 31 / 0.47
h ≈ 66 inches
Therefore, the two models give the same weight when the height is approximately 66 inches.
(c) To find the change in weight associated with a 1-inch increase in height for the first model, we subtract the weights for h and h+1:
Change in weight = (7.45(h+1) - 375) - (7.45h - 375)
Change in weight = 7.45h + 7.45 - 375 - 7.45h + 375
Change in weight = 7.45 - 375 + 375
Change in weight = 7.45
Therefore, a 1-inch increase in height is associated with a 7.45-pound increase in weight for the first model.
To find the change in weight associated with a 1-inch increase in height for the second model, we subtract the weights for h and h+1:
Change in weight = (7.92(h+1) - 406) - (7.92h - 406)
Change in weight = 7.92h + 7.92 - 406 - 7.92h + 406
Change in weight = 7.92 - 406 + 406
Change in weight = 7.92
Therefore, a 1-inch increase in height is associated with a 7.92-pound increase in weight for the second model.