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Let's solve part (b) of the problem to find the z-score for a student who is 42 years old using the given statistics.

The formula to calculate the z-score is:

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

Where:
- \( X \) is the value we want to find the z-score for (in this case, 42 years old).
- \( \mu \) is the mean (given as 30.3).
- \( \sigma \) is the standard deviation (given as 15.1).

Now, plugging in the values:

\[
z = \frac{42 - 30.3}{15.1}
\]

Let me calculate that.The z-score for a student who is 42 years old is approximately \( 0.775 \).

Do you have any questions, or would you like more details on how the calculation was done?

Here are 5 related questions to further your understanding:
1. What does the z-score represent in this context?
2. How would the z-score change if the student's age were higher or lower?
3. Why is standard deviation important in calculating the z-score?
4. How would you interpret a negative z-score?
5. How would you calculate the probability associated with a given z-score?

**Tip**: A z-score tells you how many standard deviations a particular value is from the mean. It helps in comparing values from different distributions.

Find the z-score of a student who is 42 years old using the given statistics (Mean = 30.3, Standard Deviation = 15.1).

Learn how to calculate the z-score for a student who is 42 years old, using a mean of 30.3 and a standard deviation of 15.1. This solution covers key statistical concepts such as the z-score formula, standard deviation, and mean. Suitable for students in Grades 10-12.

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