Question

Liam is 57 inches tall. His brother Aitor is 45 inches tall. For Liam's age group, the mean height is 54.5 inches with a standard deviation of 2.4 inches. For Aitor's age group, the mean height is 41.5 inches with a standard deviation of 2.7 inches. Which of the brothers is taller, relatively speaking?

a) Liam
b) Aitor
c) They are the same height
d) Cannot be determined

Answer 1

After calculating the z-scores to determine who is taller relative to their age group, Aitor has a higher z-score of 1.30 compared to Liam's 1.04, indicating that Aitor is relatively taller than Liam is for their respective age groups.

Step-by-step explanation:

To determine which of the brothers, Liam or Aitor, is taller, relatively speaking, we need to calculate their respective z-scores based on the mean and standard deviation of their age groups. A z-score indicates how many standard deviations an element is from the mean.

This is done using the formula:

Z = (X - μ) / σ

Where:

• X is the height of the person,
• μ is the mean height for their age group, and
• σ is the standard deviation for their age group.

For Liam:

Z_Liam = (57 - 54.5) / 2.4 = 2.5 / 2.4 ≈ 1.04

For Aitor:

Z_Aitor = (45 - 41.5) / 2.7 = 3.5 / 2.7 ≈ 1.30

Since Aitor's z-score is higher, he is taller relatively speaking compared to his age group than Liam is to his own age group.

Therefore, the answer is (b) Aitor.