Question

4. An anthropologist finds a femur that is 53.7 cm long. How tall was that person?

Answer 1

To estimate the height of an individual from their femur length, anthropologists use specific formulas that correlate femur length with overall body height. The femur length provided, 53.7 cm, could approximate a height of 2.01 meters, using a general conversion factor where the femur is about 26.74% of a person's height.

Step-by-step explanation:

The question asked relates to estimating an individual's height from the length of their femur. Anthropologists have indeed developed formulas to estimate the height of an individual based on the length of the femur. This is possible because there is a known correlation between femur length and overall body height. Using these established anthropometric relationships, we can make an educated guess about a person's height. For example, different formulas might be used for men and women, as well as for various populations in which average body proportions may differ.

However, without a specific formula provided, a common method used employs a multiplication factor. For instance, the femur represents approximately 26.74% of a person's height according to some studies. To estimate height from femur length: height = femur length / 0.2674. Plugging in the femur length of 53.7 cm (537 mm), the estimated height would be approximately 2009.7 mm or about 2.01 meters.

Answer 2

Given the function

`y=1.86634x\text{ + 82.2911}`

to be the relationship between the height and femur length. Where

`\begin{gathered} x\Rightarrow femur\text{ length}(cm) \\ y\Rightarrow height\text{ (cm)} \end{gathered}`

Thus, when the femur length is 53.7 cm, the height is evaluated as

`\begin{gathered} x=53.7 \\ \text{substitute for x, the value of 53.7 in the above equation.} \\ y=1.86634(53.7)\text{ + 82.2911} \\ y=100.222458+82.2911 \\ y=182.513558 \\ \cong y=182.5 \\ \end{gathered}`

Hence, the height of the person is 182.5 cm