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. Answer the following questions.
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Part 1
What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z equals StartFraction left parenthesis x minus mu right parenthesis Over sigma EndFraction
​?
mu
equals
  
enter your response here
sigma
equals
  
enter your response here
Part 2
The original pulse rates are measured with units of​ "beats per​ minute". What are the units of the corresponding z​ scores? Choose the correct choice below.
A.
The z scores are measured with units of​ "beats."
B.
The z scores are measured with units of​ "minutes per​ beat."
C.
The z scores are measured with units of​ "beats per​ minute."
D.
The z scores are numbers without units of measurement.

### Part 1: Converting Pulse Rates to Z-scores

The formula for converting a raw score \( x \) to a z-score is:

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

Where:
- \( x \) is the raw score,
- \( \mu \) is the mean, and
- \( \sigma \) is the standard deviation.

When you convert all pulse rates to z-scores:
- The mean \( \mu \) of the z-scores will always be 0. This is because the mean in the z-score formula cancels out the shift in data.
- The standard deviation \( \sigma \) of the z-scores will always be 1. This is because the standard deviation is scaled to standardize the data.

Thus, the answers for this part are:
- **Mean ( \( \mu \) )** = 0
- **Standard deviation ( \( \sigma \) )** = 1

### Part 2: Units of the Z-scores

Z-scores are dimensionless, meaning they are simply numbers that indicate how many standard deviations a value is from the mean. The raw data had units of "beats per minute," but after conversion to z-scores, the data no longer carries units because it's a standardized score.

Thus, the correct choice is:
- **D.** The z-scores are numbers without units of measurement.

Would you like more details or have any questions?

### 5 Related Questions:
1. What does a positive or negative z-score tell you about the data point?
2. How can you use z-scores to determine outliers in a dataset?
3. What is the significance of a z-score of 1, 2, or 3 in terms of standard deviations?
4. How can z-scores be used to compare data from different distributions?
5. Can z-scores be used for data that is not normally distributed?

### Tip:
Z-scores are useful for comparing data points from different distributions, as they standardize the data and remove the units.

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? Additionally, what are the units of the corresponding z scores?

Learn how to convert women's pulse rates to z-scores, given a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute. This example explains the z-score formula and the results after standardization. Suitable for students in Grades 9-12.

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