Question

The heights (in cm) and arm spans (in cm) of 31 students were measured. The association between (height) and (arm span) is shown in the scatterplot below. The equation of the line of best fit modeling this relationship is given:

y=4.5+0.977x

Mike is 172 cm tall and George is 165 cm tall. Using the model, how many centimeters longer would we expect Mike's arm span to be than George's? Round your answer to the thousandths place.

Answer 1

Answer: Mike's arm span is 7.165 cm longer than the George's one.

Explanation:

We have that the association between height and arm span is modeled by the equation

y = 4.5 + 0.977*x

where y is height and x is arm span.

Mike is 172 cm tall, so his arm span is:

172cm = 4.5 + 0.977*x

x = (172 - 4.5)/0.977 = 171.443 cm

and George is 165 cm tall, so his arm span is:

x = (165 - 4.5)/0.977 = 164.278 cm

Then the difference between their arm span is:

171.443cm - 164.278cm = 7.165 cm

So Mike's arm span is 7.165 cm longer than the George's one.