Use z scores to compare the given values.
Based on sample​ data, newborn males have weights with a mean of 3261.6 g and a standard deviation of 600.6 g. Newborn females have weights with a mean of 3052.2 g and a standard deviation of 712.6 g. Who has the weight that is more extreme relative to the group from which they​ came: a male who weighs 1700 g or a female who weighs 1700 ​g?

To determine which weight is more extreme relative to their respective groups, we can use the z-score formula. The z-score measures how many standard deviations a value is away from the mean. The formula for calculating the z-score is:

\[
z = \frac{X - \mu}{\sigma}
\]

where:
- \( X \) is the value being compared,
- \( \mu \) is the mean of the group, and
- \( \sigma \) is the standard deviation of the group.

### Step 1: Calculate the z-score for the male newborn

Given:
- Mean (\( \mu \)) for males = 3261.6 g
- Standard deviation (\( \sigma \)) for males = 600.6 g
- Weight of the male newborn (\( X \)) = 1700 g

Substituting these values into the formula:

\[
z_{\text{male}} = \frac{1700 - 3261.6}{600.6} = \frac{-1561.6}{600.6} \approx -2.60
\]

### Step 2: Calculate the z-score for the female newborn

Given:
- Mean (\( \mu \)) for females = 3052.2 g
- Standard deviation (\( \sigma \)) for females = 712.6 g
- Weight of the female newborn (\( X \)) = 1700 g

Substituting these values into the formula:

\[
z_{\text{female}} = \frac{1700 - 3052.2}{712.6} = \frac{-1352.2}{712.6} \approx -1.90
\]

### Step 3: Compare the z-scores

- The z-score for the male newborn is \(-2.60\).
- The z-score for the female newborn is \(-1.90\).

### Conclusion

The male newborn has a z-score of \(-2.60\), which is lower than the female's z-score of \(-1.90\). This means the male's weight is more extreme relative to the mean of his group compared to the female's weight relative to her group.

### Answer

**The male who weighs 1700 g has a weight that is more extreme relative to his group.**

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Would you like to explore more details or have any questions? Here are some related questions you might find interesting:

1. How is the z-score used to determine how unusual a value is?
2. What is the significance of a negative z-score?
3. How do you interpret z-scores in different contexts?
4. Can z-scores be used to compare different types of data?
5. What does it mean if two values have the same z-score?

**Tip:** The farther a z-score is from zero, the more unusual the value is compared to the mean.

Based on sample data, newborn males have weights with a mean of 3261.6 g and a standard deviation of 600.6 g. Newborn females have weights with a mean of 3052.2 g and a standard deviation of 712.6 g. Who has the weight that is more extreme relative to the group from which they came: a male who weighs 1700 g or a female who weighs 1700 g?

Find out how to compare z-scores for newborn male and female weights using sample data. We calculate the z-scores based on given means and standard deviations for both genders to determine which weight is more extreme. Suitable for high school statistics students.

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