The average height of American adult males is 177 cm , with a standard deviation of 7.4 cm . Meanwhile, the average height of Indian males is 165 cm , with a standard deviation of 6.7 cm . Which is taller relative to his nationality, a \( 168-\mathrm{cm} \) American man or a \( 157-\mathrm{cm} \) Indian man?

To determine which individual is taller relative to their nationality, we can use **z-scores**. A z-score indicates how many standard deviations an element is from the mean. A higher z-score means the individual is taller relative to their group's average. **Calculations:** 1. **American Man:** - **Mean (μ_A):** 177 cm - **Standard Deviation (σ_A):** 7.4 cm - **Height (X_A):** 168 cm - **Z-score (z_A):** \[ z_A = \frac{X_A - μ_A}{σ_A} = \frac{168 - 177}{7.4} \approx -1.216 \] 2. **Indian Man:** - **Mean (μ_I):** 165 cm - **Standard Deviation (σ_I):** 6.7 cm - **Height (X_I):** 157 cm - **Z-score (z_I):** \[ z_I = \frac{X_I - μ_I}{σ_I} = \frac{157 - 165}{6.7} \approx -1.194 \] **Interpretation:** - The **American man** has a z-score of approximately **-1.216**, meaning he is about **1.216 standard deviations below** the American average. - The **Indian man** has a z-score of approximately **-1.194**, meaning he is about **1.194 standard deviations below** the Indian average. Since the Indian man's z-score is closer to zero, he is **less below** his national average compared to the American man. Therefore: **Conclusion:** The \(157\)-cm Indian man is taller relative to his nationality than the \(168\)-cm American man.