A certain distribution has a mean of 32 and a standard deviation of 4. Find the z-score for a value of 20. Z-Score = [?]

To find the z-score for a value of 20, use the z-score formula:

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

where:
- \( X = 20 \) (the value for which we're finding the z-score),
- \( \mu = 32 \) (the mean of the distribution),
- \( \sigma = 4 \) (the standard deviation).

Substitute the values into the formula:

\[
z = \frac{20 - 32}{4} = \frac{-12}{4} = -3
\]

So, the z-score for a value of 20 is:

\[
z = -3
\]

Would you like further explanation or have any questions?

Here are some related questions you might find useful:
1. How do you interpret a z-score of -3 in terms of standard deviations from the mean?
2. What is the probability of finding a value less than 20 in this distribution?
3. How would the z-score change if the value were closer to the mean, like 28?
4. How does the z-score formula apply to non-normal distributions?
5. What does a positive z-score indicate compared to a negative one?

**Tip:** Remember, a z-score tells you how many standard deviations a value is from the mean, allowing comparisons across different distributions.

Find the z-score for a value of 20 in a distribution with a mean of 32 and a standard deviation of 4. This problem demonstrates how to apply the z-score formula, which measures the number of standard deviations a data point is from the mean. Perfect for students learning about normal distributions and standard scores in Grades 9-11.

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