Use the standard normal table to find the​ z-score that corresponds to the given percentile. If the area is not in the​ table, use the entry closest to the area. If the area is halfway between two​ entries, use the​ z-score halfway between the corresponding​ z-scores. If​ convenient, use technology to find the​ z-score.
Upper P 8
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Part 1
The​ z-score that corresponds to Upper P 8 is 
  
enter your response here. 
​(Round to two decimal places as​ needed.)

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.

Use the standard normal table to find the​ z-score that corresponds to the given percentile. If the area is not in the​ table, use the entry closest to the area. If the area is halfway between two​ entries, use the​ z-score halfway between the corresponding​ z-scores. If​ convenient, use technology to find the​ z-score. Upper P 8

Learn how to find the z-score corresponding to the 8th percentile using the standard normal distribution table. This step-by-step guide demonstrates how to interpret percentiles and z-scores and how to use the z-table effectively. Suitable for high school students in Grades 10-12.

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