A population has mean μ=20 and standard deviation σ=4. Round the answers to two decimal places as needed.

(a) Find the Z-score for a population value of 6.

The Z-score for a population value of 6 is

To find the Z-score of a population value, we use the formula:

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

where:
- \( X \) is the population value,
- \( \mu \) is the mean,
- \( \sigma \) is the standard deviation.

Given:
- \( X = 6 \)
- \( \mu = 20 \)
- \( \sigma = 4 \)

Substitute these values into the formula:

\[
Z = \frac{6 - 20}{4}
\]

Let's calculate this.The Z-score for a population value of 6 is \(-3.5\).

Would you like more details or have any questions about this? 

Here are 5 related questions that expand on this information:
1. How do you interpret a negative Z-score?
2. What is the Z-score for a population value of 25 with the same mean and standard deviation?
3. What percentage of the population lies below a Z-score of -3.5?
4. How does changing the standard deviation affect the Z-score?
5. What does a Z-score represent in a standard normal distribution?

**Tip:** A Z-score tells you how many standard deviations a data point is from the mean. A negative Z-score means the data point is below the mean.

A population has mean μ=20 and standard deviation σ=4. Find the Z-score for a population value of 6.

Discover how to calculate the Z-score for a population value of 6, given a mean of 20 and a standard deviation of 4. This step-by-step guide explains the Z-score formula and its significance in a standard normal distribution. Ideal for students in Grades 9-12.

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