Question 28, *3.4.7 Save In a certain city, the average 20- to 29-year old man is 72.5 inches tall, with a standard deviation of 3.1 inches, while the average 20 - to 29 -year old woman is 64.5 inches tall, with a standard deviation of 3.8 inches. Who is relatively taller, a 75 -inch man or a 70 -inch woman? Who is relatively taller, a 75-inch man or a 70 -inch woman? A. The z-score for the man is larger, so he is relatively taller. B. The z-score for the woman is larger, so she is relatively taller. C. The z-score for the man is smaller, so he is relatively taller. D. The z-score for the woman is smaller, so she is relatively taller.

To determine who is relatively taller, we can calculate the **z-scores** for both the man and the woman. The z-score tells us how many standard deviations an individual is from the mean. **For the man:** - **Mean height (μ₁):** 72.5 inches - **Standard deviation (σ₁):** 3.1 inches - **Man's height (X₁):** 75 inches \[ z_1 = \frac{X_1 - \mu_1}{σ_1} = \frac{75 - 72.5}{3.1} \approx \frac{2.5}{3.1} \approx 0.806 \] **For the woman:** - **Mean height (μ₂):** 64.5 inches - **Standard deviation (σ₂):** 3.8 inches - **Woman's height (X₂):** 70 inches \[ z_2 = \frac{X₂ - μ₂}{σ₂} = \frac{70 - 64.5}{3.8} \approx \frac{5.5}{3.8} \approx 1.447 \] **Comparison:** - **Man's z-score:** ≈ 0.806 - **Woman's z-score:** ≈ 1.447 The woman has a higher z-score, meaning she is **relatively taller** compared to her peer group than the man is to his. **Answer:** **B. The z-score for the woman is larger, so she is relatively taller.**