https://file.aiquickdraw.com/mathbot/file/1726326790265azbo8fqu.jpg

To solve this problem, we need to calculate the z-scores for both babies in the 35-week and 40-week gestation periods. The formula for a z-score is:

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

Where:
- \( X \) is the baby's weight,
- \( \mu \) is the mean weight for that gestation period,
- \( \sigma \) is the standard deviation for that gestation period.

### For the baby born at 35 weeks:
- \( X = 2750 \) grams,
- \( \mu = 2900 \) grams,
- \( \sigma = 900 \) grams.

Now let's compute the z-score for this baby.

### For the baby born at 40 weeks:
- \( X = 3250 \) grams,
- \( \mu = 3400 \) grams,
- \( \sigma = 435 \) grams.

We'll also compute the z-score for this baby.

Let's proceed with these calculations.The z-scores are as follows:

- For the baby born at 35 weeks, the z-score is approximately \(-0.17\).
- For the baby born at 40 weeks, the z-score is approximately \(-0.34\).

### Interpretation:
- The baby born at 35 weeks has a z-score closer to zero, indicating that its weight is closer to the mean compared to the baby born at 40 weeks.
- The baby born at 40 weeks has a z-score that is lower, indicating that its weight is further from the mean and relatively lighter than the baby born at 35 weeks in terms of standard deviation.

Would you like more details or further clarification on any part of this solution?

Here are 5 related questions you can explore:
1. What is the significance of a z-score in statistics?
2. How do different standard deviations affect the z-score for babies born at different gestation periods?
3. What does a positive z-score represent in this context?
4. How would the z-scores change if the weights of the babies were higher than the mean?
5. Why is it important to standardize values using z-scores in real-world applications?

**Tip:** A z-score of 0 means the data point is exactly at the mean value. Negative or positive values show how far and in which direction the data point is from the mean.

Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2900 grams and a standard deviation of 900 grams while babies born after a gestation period of 40 weeks have a mean weight of 3400 grams and a standard deviation of 435 grams. If a 35-week gestation period baby weighs 2750 grams and a 40-week gestation period baby weighs 3250 grams, find the corresponding z-scores. Which baby weighs relatively less since its z-score?

Learn how to calculate and compare z-scores for baby weights at different gestation periods. This detailed guide includes step-by-step calculations using mean, standard deviation, and the z-score formula. Suitable for college-level statistics courses.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation