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The questions in the image ask for the Z-scores based on standard deviations from the mean.

Let's address each:

1. **What is the Z-score of \( x = 6 \) if it is 2.9 standard deviations to the left of the mean?**

   - Z-scores measure how many standard deviations a value is from the mean. If \( x \) is 2.9 standard deviations to the **left** of the mean, the Z-score is negative.
   - So, the Z-score for \( x = 6 \) is:
     \[
     z = -2.9
     \]

2. **What is the Z-score of \( x = 11 \) if it is 2.4 standard deviations to the right of the mean?**

   - Since \( x = 11 \) is 2.4 standard deviations to the **right** of the mean, the Z-score is positive.
   - So, the Z-score for \( x = 11 \) is:
     \[
     z = 2.4
     \]

### Would you like more details on how Z-scores are calculated, or do you have other questions?

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Here are 5 relative questions to expand understanding:

1. What is a Z-score and why is it important in statistics?
2. How do you calculate the Z-score if you know the value of \( x \), the mean, and the standard deviation?
3. What does a Z-score of 0 indicate?
4. How would the Z-score change if the standard deviation increases but \( x \) stays the same?
5. Can you explain how Z-scores are used to find probabilities in a normal distribution?

**Tip**: A Z-score tells you how unusual or typical a data point is within a distribution by measuring the distance (in standard deviations) from the mean.

What is the Z-score of x = 6 if it is 2.9 standard deviations to the left of the mean? What is the Z-score of x = 11 if it is 2.4 standard deviations to the right of the mean?

Learn how to calculate the Z-scores of x = 6 and x = 11 when they are 2.9 and 2.4 standard deviations away from the mean, respectively. This guide covers key concepts of Z-scores and standard deviation in a normal distribution. Suitable for students in Grades 9-12.

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