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When converting a dataset to z-scores using the formula:

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

where \( \mu \) is the mean and \( \sigma \) is the standard deviation, the mean of the z-scores will always be 0, and the standard deviation will always be 1. This transformation standardizes the dataset, centering it at 0 and scaling it to have a standard deviation of 1.

Thus, after converting all pulse rates of women to z-scores:

- \( \mu = 0 \)
- \( \sigma = 1 \)

Would you like a detailed explanation or have any questions?

Here are five related questions:
1. What is the significance of converting a dataset to z-scores?
2. How would you interpret a z-score of 1.5 in this context?
3. What happens to the shape of the distribution when data is converted to z-scores?
4. Can z-scores be used to identify outliers? If so, how?
5. How would you standardize a dataset that does not follow a normal distribution?

**Tip:** Z-scores are useful for comparing data points from different distributions because they convert values to a common scale.

Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute. What are the values of the mean and standard deviation after converting all pulse rates of women to z-scores?

Learn how to standardize a set of data, such as the pulse rates of women, by converting them to z-scores. After converting, the mean becomes 0 and the standard deviation becomes 1, helping you interpret data points more easily. Ideal for students in Grades 9-12.

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