Question

USE TOOLS Forensic scientists use the equation h = 2.4f + 46.2 to estimate the

height h of a woman given the length in centimeters f of her femur bone.
Suppose the equation has a margin of error of 3 centimeters. Could a female
femur bone measuring 47 centimeters be that of a woman who was
170 centimeters tall?

Answer 1

No

Explanation:

To determine if a female femur bone measuring 47 centimeters could belong to a woman who was 170 centimeters tall, we can use the given equation with a margin of error.

The equation is h = 2.4f + 46.2, where h is the estimated height, and f is the length of the femur bone. If the equation has a margin of error of 3 centimeters then:

`2.4f + 46.2 - 3 < h < 2.4f + 46.2 + 3`

`2.4f + 43.2 < h < 2.4f + 49.2`

Now, substitute the given femur length (f = 47) into the inequality:

`2.4(47) + 43.2 < h < 2.4(47) + 49.2`

`112.8 + 43.2 < h < 112.8 + 49.2`

`156 < h < 162`

So, the estimated height range of a woman with a femur bone measuring 47 centimeters is from 156 to 162 centimeters.

Therefore, based on the equation and considering the margin of error, it is improbable that a female femur bone measuring 47 centimeters could be associated with a woman who was 170 centimeters tall.