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The problem involves a normal distribution and a z-score. Let's break it down:

- The random variable \( X \) follows a normal distribution with mean 22 and standard deviation 1, i.e., \( X \sim N(22, 1) \).
- A z-score of 0 corresponds to the realization of \( X \) (denoted as \( x_i \)) that is exactly at the mean of the distribution. This is because the z-score formula is given by:

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

where \( \mu \) is the mean and \( \sigma \) is the standard deviation. If \( z = 0 \), then:

\[
0 = \frac{x_i - 22}{1} \implies x_i = 22
\]

Therefore, for a z-score of 0, the value of \( x_i \) is equal to the mean, which is 22.

The correct answer is 22.

Would you like further details or have any questions? Here are some related questions:

1. What does a z-score represent in a normal distribution?
2. How do you calculate a z-score for any value?
3. What does a z-score of 1 or -1 indicate about a value relative to the mean?
4. How does changing the standard deviation affect the z-scores?
5. How can you interpret z-scores when dealing with empirical data?

**Tip:** Z-scores are a useful way to standardize values, allowing you to compare data points across different normal distributions.

Consider a random variable X~N(22,1). For a z-score equal to 0, what is the value of this realization of the random variable X (i.e., xi)?

Learn how to find the realization of a random variable X~N(22,1) for a z-score of 0. Understand the use of the z-score formula and its application to normal distributions. Suitable for Grades 10-12.

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