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 () using the standard normal distribution, we need to determine the value of such that the area to the left of is 0.08 (since the 8th percentile means that 8% of the data lies below that point).
- Look at the standard normal (z) table or use technology to find the z-score for an area of 0.08.
- 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 .
Thus, the z-score that corresponds to the 8th percentile is .
Would you like further details or have any questions?
Here are 5 follow-up questions that can help expand your understanding:
- How do you interpret a z-score in terms of standard deviations from the mean?
- What is the z-score for the 50th percentile (median)?
- How can you use the z-score to find probabilities for different percentiles?
- How would you find the z-score for a percentile not listed in a z-table?
- 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
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