Round each z-score to the nearest hundredth.

A data set has a mean of 
x = 71
 and a standard deviation of 10.1. Find the z-score for each of the following.

To calculate the z-score for each value, you use the z-score formula:

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

where:
- \( x \) is the value in the data set,
- \( \mu \) is the mean of the data set,
- \( \sigma \) is the standard deviation of the data set.

Given:
- Mean (\( \mu \)) = 71
- Standard deviation (\( \sigma \)) = 10.1

Please provide the values for which you want to calculate the z-scores, and I can help you calculate and round them to the nearest hundredth.

Would you like to proceed with specific values?

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Here are some questions you might explore after calculating z-scores:
1. What does the z-score tell us about a data point's position in a normal distribution?
2. How does a higher or lower z-score affect the interpretation of data points?
3. How would you interpret a z-score of 0?
4. What would a z-score of ±2.5 suggest about a data point's location relative to the mean?
5. Can z-scores be used for comparing data sets with different means and standard deviations?

**Tip**: Z-scores standardize different data sets, making them comparable across different scales.

Round each z-score to the nearest hundredth.

A data set has a mean of 71 and a standard deviation of 10.1. Find the z-score for each of the following.

Learn how to calculate z-scores for a data set with a mean of 71 and a standard deviation of 10.1. This page explains the z-score formula and its application to standardize values, with step-by-step guidance on rounding z-scores to the nearest hundredth. Ideal for high school students in Grades 9-12.

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