To find the z-score corresponding to the 20th percentile (P20) using the standard normal distribution table, you follow these steps:

1. Find the area under the standard normal curve that corresponds to 0.20, since P20 represents the area to the left of the z-score.

2. Locate the closest value to 0.20 in the body of the z-table, which provides cumulative probabilities from the left. The closest area to 0.20 is 0.2005.

3. The corresponding z-score for this cumulative probability is -0.84.

Thus, the z-score that corresponds to P20 is -0.84 (rounded to two decimal places).

Would you like further explanation or have any additional questions? Here are five related questions you might find useful:

1. How do you interpret a z-score of -0.84 in context of standard normal distribution?
2. How can you use technology like a calculator or software to find z-scores more efficiently?
3. What is the z-score corresponding to the 50th percentile (P50)?
4. How do you calculate a z-score if given a value from a non-standard normal distribution?
5. What is the significance of percentiles in statistics?

Tip: When working with z-scores and percentiles, it’s helpful to remember that the standard normal distribution is symmetric around 0, so percentiles less than 50 will correspond to negative z-scores.