Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 3000 grams and a standard deviation of 900 grams while babies born after a gestation period of 40 weeks have a mean weight of 3600 grams and a standard deviation of 590 grams. If a 33-week gestation period baby weighs 3375 grams and a 41-week gestation period baby weighs 3975 ​grams, find the corresponding​ z-scores. Which baby weighs more relative to the gestation​ period?

To find the z-scores for both babies, we can use the following formula for the z-score:

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

where:
- \(x\) is the observed value (the baby's weight),
- \(\mu\) is the mean weight for that gestation period,
- \(\sigma\) is the standard deviation for that gestation period.

### Baby born after 33 weeks:

For the 33-week gestation period baby:
- \(x = 3375 \, \text{grams}\),
- \(\mu = 3000 \, \text{grams}\),
- \(\sigma = 900 \, \text{grams}\).

The z-score for this baby is:
\[
z = \frac{3375 - 3000}{900} = \frac{375}{900} \approx 0.42
\]

### Baby born after 41 weeks:

For the 41-week gestation period baby:
- \(x = 3975 \, \text{grams}\),
- \(\mu = 3600 \, \text{grams}\),
- \(\sigma = 590 \, \text{grams}\).

The z-score for this baby is:
\[
z = \frac{3975 - 3600}{590} = \frac{375}{590} \approx 0.64
\]

### Conclusion:

- The z-score for the 33-week gestation baby is approximately 0.42.
- The z-score for the 41-week gestation baby is approximately 0.64.

Since the 41-week gestation baby has a higher z-score, this baby weighs more relative to the gestation period compared to the 33-week gestation baby.

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Would you like further clarification or details? 

Here are 5 related questions to consider:
1. What is the significance of a higher z-score in this context?
2. How would z-scores help compare more than two babies with different gestation periods?
3. What does a z-score of 0 mean in terms of baby weight?
4. How would the z-scores change if we adjusted the standard deviations?
5. How could we interpret a negative z-score in this situation?

**Tip**: Z-scores are useful in comparing values across different distributions by standardizing them.

Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 3000 grams and a standard deviation of 900 grams while babies born after a gestation period of 40 weeks have a mean weight of 3600 grams and a standard deviation of 590 grams. If a 33-week gestation period baby weighs 3375 grams and a 41-week gestation period baby weighs 3975 grams, find the corresponding z-scores. Which baby weighs more relative to the gestation period?

Find out how to calculate the z-scores for babies born after 33 and 41-week gestation periods. This problem covers statistical concepts like normal distribution and standard deviation, using the formula Z = (x - μ) / σ. Learn which baby weighs more relative to the gestation period. Suitable for Grades 11-12.

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