To determine who has the weight that is more extreme relative to their respective group, we need to calculate the z-scores for both the male and female newborns and then compare them.
### Male Newborn's Z-score Calculation
Given:
- Mean weight of newborn males ([tex]\(\mu_{\text{male}}\)[/tex]): 3227.2 g
- Standard deviation of newborn males ([tex]\(\sigma_{\text{male}}\)[/tex]): 547.2 g
- Weight of the male newborn: 1700 g
The z-score formula is:
[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]
For the male newborn:
[tex]\[ z_{\text{male}} = \frac{1700 - 3227.2}{547.2} \][/tex]
From this calculation, the z-score for the male newborn is:
[tex]\[ z_{\text{male}} = -2.79 \][/tex]
### Female Newborn's Z-score Calculation
Given:
- Mean weight of newborn females ([tex]\(\mu_{\text{female}}\)[/tex]): 3089.2 g
- Standard deviation of newborn females ([tex]\(\sigma_{\text{female}}\)[/tex]): 742.7 g
- Weight of the female newborn: 1700 g
Using the z-score formula again:
[tex]\[ z_{\text{female}} = \frac{1700 - 3089.2}{742.7} \][/tex]
From this calculation, the z-score for the female newborn is:
[tex]\[ z_{\text{female}} = -1.87 \][/tex]
### Comparison of Z-scores
The absolute values of the z-scores are:
[tex]\[ |z_{\text{male}}| = 2.79 \][/tex]
[tex]\[ |z_{\text{female}}| = 1.87 \][/tex]
Since the absolute value of the male's z-score (2.79) is greater than that of the female's z-score (1.87), the weight of the male newborn is more extreme relative to the group.
### Final Answer
Since the [tex]\( z \)[/tex] score for the male is [tex]\( z = -2.79 \)[/tex] and the [tex]\( z \)[/tex] score for the female is [tex]\( z = -1.87 \)[/tex], the male has the weight that is more extreme.
