A population with u = 85 and o = 12 is transformed into z-scores. After the transformation, what is the standard deviation for the population of z-scores?

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**Question 6:**  
A population with a mean (\(\mu\)) of 85 and a standard deviation (\(\sigma\)) of 12 is transformed into z-scores. After the transformation, what is the standard deviation for the population of z-scores?

**Explanation:**

In statistics, z-scores are used to describe a value's position in relation to the mean of a group of values. Z-scores are calculated using the formula:

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

Where:
- \(X\) is the value being transformed,
- \(\mu\) is the mean of the population,
- \(\sigma\) is the standard deviation of the population.

When a population is transformed into z-scores:
- The mean of the z-scores is always 0.
- The standard deviation of the z-scores is always 1.

Thus, after the transformation, the standard deviation for the population of z-scores is 1.
Transcribed Image Text:**Question 6:** A population with a mean (\(\mu\)) of 85 and a standard deviation (\(\sigma\)) of 12 is transformed into z-scores. After the transformation, what is the standard deviation for the population of z-scores? **Explanation:** In statistics, z-scores are used to describe a value's position in relation to the mean of a group of values. Z-scores are calculated using the formula: \[ z = \frac{X - \mu}{\sigma} \] Where: - \(X\) is the value being transformed, - \(\mu\) is the mean of the population, - \(\sigma\) is the standard deviation of the population. When a population is transformed into z-scores: - The mean of the z-scores is always 0. - The standard deviation of the z-scores is always 1. Thus, after the transformation, the standard deviation for the population of z-scores is 1.
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