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 20
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Part 1
The​ z-score that corresponds to Upper P 20 is 
  
enter your response here. 
​(Round to two decimal places as​ needed.)

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.

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 20

Learn how to find the z-score that corresponds to the 20th percentile (P20) using the standard normal distribution table. This step-by-step guide explains key statistical concepts like z-scores, percentiles, and properties of the standard normal distribution. Perfect for high school students studying statistics.

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