Use z scores to compare the given values. Based on sample data, newborn males have weights with a mean of 3235.6 g and a standard deviation of 722.5 g . Newborn females have weights with a mean of 3074.2 g and a standard deviation of 578.2 g . Who has the weight that is more extreme relative to the group from which they came: a male who weighs 1600 g or a female who weighs 1600 g ? Since the z score for the male is \( \mathrm{z}=\square \) and the z score for the female is \( \mathrm{z}=\square \), the \( \square \) has the weight that is more extreme. (Round to two decimal places.)

To determine which weight is more extreme relative to its respective group, we calculate the **z-scores** for both the male and female newborns weighing **1600 g**. ### Given Data: - **Male Newborns:** - Mean (\( \mu_m \)) = 3235.6 g - Standard Deviation (\( \sigma_m \)) = 722.5 g - **Female Newborns:** - Mean (\( \mu_f \)) = 3074.2 g - Standard Deviation (\( \sigma_f \)) = 578.2 g ### Z-Score Formula: \[ z = \frac{X - \mu}{\sigma} \] where: - \( X \) = observed value - \( \mu \) = mean - \( \sigma \) = standard deviation ### Calculations: 1. **Male Newborn:** \[ z_m = \frac{1600 - 3235.6}{722.5} = \frac{-1635.6}{722.5} \approx -2.26 \] 2. **Female Newborn:** \[ z_f = \frac{1600 - 3074.2}{578.2} = \frac{-1474.2}{578.2} \approx -2.55 \] ### Interpretation: - **Absolute Z-Scores:** - \(|z_m| = 2.26\) - \(|z_f| = 2.55\) A higher absolute z-score indicates a value is more extreme relative to its group. ### Conclusion: Since \( |z_f| > |z_m| \), the **female newborn** has the weight that is more extreme relative to her group. **Final Answer:** Since the z score for the male is \( \mathrm{z}=-2.26 \) and the z score for the female is \( \mathrm{z}=-2.55 \), the **female** has the weight that is more extreme.