Math Problem Statement

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 Click to view page 1 of the table.LOADING... Click to view page 2 of the table.LOADING... Question content area bottom Part 1 The​ z-score that corresponds to Upper P 8 is    enter your response here. ​(Round to two decimal places as​ needed.)

Solution

To find the z-score that corresponds to the 8th percentile (P8P_8) using the standard normal distribution, we need to determine the value of zz such that the area to the left of zz 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 1.41-1.41.

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

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Math Problem Analysis

Mathematical Concepts

Statistics
Standard Normal Distribution
Percentiles
Z-Scores

Formulas

Z-Score formula
Percentile to Z-Score mapping

Theorems

Properties of the Standard Normal Distribution

Suitable Grade Level

Grades 10-12