To find the z-score of the item $x = 130$ given the mean $\mu = 110$ and standard deviation $\sigma = 8$, we use the z-score formula:

$z = \frac{x - \mu}{\sigma}$

Substituting the values:

$z = \frac{130 - 110}{8}$

$z = \frac{20}{8} = 2.5$

Final Answer:

The z-score is 2.5.

Would you like me to explain how to interpret this z-score or go into more details?

Here are 5 related questions to deepen your understanding:

1. What does a positive z-score indicate in a distribution?
2. How would the z-score change if the standard deviation were smaller?
3. What is the z-score for an item $x = 102$ with the same mean and standard deviation?
4. How do z-scores help compare values from different distributions?
5. What percentage of the data falls below a z-score of $2.5$ in a normal distribution?

Tip: A z-score tells you how many standard deviations a value is away from the mean. Positive z-scores are above the mean, and negative z-scores are below the mean.