https://file.aiquickdraw.com/mathbot/file/17271865626055z64s2wh.jpg

help me solve this with right formula in each box

The image you uploaded contains two main formulas used in statistics:

1. **Part 1: Calculate \( z \) (Z-score)**:  
   The formula is:
   \[
   z = \frac{X - \mu}{SD}
   \]
   - \( X \) is the observed value.
   - \( \mu \) is the mean.
   - \( SD \) is the standard deviation.

   To calculate the Z-score, you need to plug in the values of \( X \), \( \mu \), and \( SD \) into this formula.

2. **Part 2: Find the X-value given a Z-score**:  
   The formula is:
   \[
   X = \mu + (z \cdot SD)
   \]
   - \( z \) is the given Z-score.
   - \( \mu \) is the mean.
   - \( SD \) is the standard deviation.

To help you input the correct formulas into the boxes provided:

### Part 1:
For calculating \( z \):
- The formula for calculating \( z \) should be entered as:  
   \[
   z = \frac{X - \mu}{SD}
   \]

### Part 2:
For calculating \( X \) from a given Z-score:
- The formula for calculating \( X \) should be entered as:  
   \[
   X = \mu + (z \cdot SD)
   \]

Once you input the correct values for \( X \), \( \mu \), and \( SD \), these formulas will give you the result for the Z-score in Part 1 and the X-value in Part 2.

Let me know if you'd like to solve a specific example or need further clarification.

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### 5 Related Questions:
1. How do you interpret the Z-score once it's calculated?
2. What does a high or low Z-score indicate about the data point?
3. How can you use the Z-score to compare data from different distributions?
4. What are the implications if the Z-score is negative?
5. How do you calculate the standard deviation if only raw data is provided?

### Tip:
The Z-score represents how many standard deviations a data point is from the mean. This is helpful in comparing data points from different datasets with different means and standard deviations.

Learn how to calculate Z-scores and X-values using the formulas z = (X - μ) / SD and X = μ + (z × SD). These calculations involve mean (μ) and standard deviation (SD), essential in statistics for interpreting data. This is suitable for students in Grades 9-12.

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