https://file.aiquickdraw.com/mathbot/file/1727186780429ub4pbdc1.jpg

type in X:
type in Mean (*μ*):
type in SD:

calculate z Type formula here:

The image provides information for calculating z-scores and finding weights using the z-score formula. Here is a breakdown of how to approach these calculations:

### Given Data:
- Mean birth weight (µ) = 7.17 lbs
- Standard deviation (SD) = 1.24 lbs

### Formula for Z-Score:
The z-score is calculated using the formula:
\[
z = \frac{X - \mu}{\text{SD}}
\]
where:
- \( X \) is the observed value (the weight in this case),
- \( \mu \) is the mean,
- SD is the standard deviation.

### Steps to Answer the Questions:

#### a) Z-Score for 8.00 lbs:
\[
z = \frac{8.00 - 7.17}{1.24}
\]

#### b) Z-Score for 4.50 lbs:
\[
z = \frac{4.50 - 7.17}{1.24}
\]

#### c) Weight (in lbs) for z = +2.50:
For this, rearrange the z-score formula to solve for \( X \):
\[
X = z \times \text{SD} + \mu
\]
For \( z = +2.50 \):
\[
X = 2.50 \times 1.24 + 7.17
\]

#### d) Weight (in lbs) for z = 0:
Since \( z = 0 \) means the weight is at the mean:
\[
X = \mu = 7.17 \, \text{lbs}
\]

I'll calculate the values for you next.Here are the results for the questions:

1. **Z-scores**:
   - a) The z-score for a birth weight of 8.00 lbs is approximately **0.67**.
   - b) The z-score for a birth weight of 4.50 lbs is approximately **-2.15**.

2. **Weights**:
   - c) The weight corresponding to a z-score of +2.50 is **10.27 lbs**.
   - d) The weight corresponding to a z-score of 0 is **7.17 lbs** (the mean).

Do you have any further questions or would you like more details?

Here are 5 related questions you could explore:
1. What does a positive or negative z-score indicate in terms of birth weight?
2. How would you calculate the birth weight for a z-score of -1.5?
3. How can z-scores be used to compare weights in different populations?
4. What percentage of infants are expected to have a birth weight below 4.50 lbs?
5. How would the z-score change if the standard deviation were larger?

**Tip:** A z-score tells you how many standard deviations an observation is from the mean.

Find the z-scores and corresponding weights based on the given birth weight statistics (mean = 7.17 lbs, SD = 1.24 lbs).

Learn how to calculate z-scores and find corresponding birth weights for given z-scores based on a normal distribution with a mean of 7.17 lbs and a standard deviation of 1.24 lbs. Step-by-step solutions provided.

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