To find the z-score that corresponds to the 8th percentile ($P_8$) using the standard normal distribution, we need to determine the value of $z$ such that the area to the left of $z$ is 0.08 (since the 8th percentile means that 8% of the data lies below that point).

1. Look at the standard normal (z) table or use technology to find the z-score for an area of 0.08.
2. In most z-tables, we search for the closest area, which is 0.08. The corresponding z-score for an area of 0.08 is approximately $-1.41$.

Thus, the z-score that corresponds to the 8th percentile is $\mathbf{-1.41}$.

Would you like further details or have any questions?

Here are 5 follow-up questions that can help expand your understanding:

1. How do you interpret a z-score in terms of standard deviations from the mean?
2. What is the z-score for the 50th percentile (median)?
3. How can you use the z-score to find probabilities for different percentiles?
4. How would you find the z-score for a percentile not listed in a z-table?
5. How is the z-score related to the concept of a standard normal distribution?

Tip: A negative z-score indicates a value below the mean, while a positive z-score indicates a value above the mean.