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The image contains a statistics question about converting pulse rates into z-scores. Here's a breakdown:

**Given Information:**
- Pulse rates of women are normally distributed with:
  - Mean (μ) = 77.5 beats per minute
  - Standard deviation (σ) = 11.6 beats per minute
- The z-score formula is \( z = \frac{(x - \mu)}{\sigma} \), where:
  - \( x \) is the value of the pulse rate
  - \( \mu \) is the mean pulse rate
  - \( \sigma \) is the standard deviation

After converting all pulse rates to z-scores, the new distribution will have:
- Mean of \( \mu_z = 0 \)
- Standard deviation of \( \sigma_z = 1 \)

**Question:**
What are the units of the corresponding z-scores?

### Answer Options:
- A: The z-scores are measured with units of "beats."
- B: The z-scores are measured with units of "beats per minute."
- C: The z-scores are measured with units of "minutes per beat."
- D: The z-scores are numbers without units of measurement.

### **Correct Answer:**
**D: The z-scores are numbers without units of measurement.**

Z-scores are dimensionless because they represent the number of standard deviations a data point is from the mean, not a quantity with units.

Would you like further clarification or a deeper explanation?

### Follow-up Questions:
1. What does a z-score of 0 indicate about a data point?
2. How do you interpret positive versus negative z-scores?
3. Why is the z-score distribution standardized to have a mean of 0 and a standard deviation of 1?
4. How would you calculate the z-score for a pulse rate of 85 beats per minute?
5. What is the significance of a z-score beyond ±3?

**Tip:** Z-scores are particularly useful for comparing data from different distributions by standardizing them into a common scale.

The original pulse rates are measured with units of 'beats per minute'. What are the units of the corresponding z-scores?

This problem demonstrates how to convert pulse rates into z-scores using the formula z = (x - μ) / σ, where pulse rates are normally distributed. The units of z-scores are dimensionless numbers, and this concept is suitable for high school statistics students (Grades 10-12).

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