Math Problem Statement

In a normal distribution, a data value located 0.7 standard deviations below the mean has Standard Score: z = 

In a normal distribution, a data value located 2.5 standard deviations above the mean has Standard Score: z = 

In a normal distribution, the mean has Standard Score: z = 

Solution

In a normal distribution, the standard score (z-score) is calculated based on how many standard deviations a data value is from the mean.

  1. A data value located 0.7 standard deviations below the mean has a z-score of: z=0.7z = -0.7

  2. A data value located 2.5 standard deviations above the mean has a z-score of: z=2.5z = 2.5

  3. The mean of the distribution has a z-score of: z=0z = 0

If you have any questions or need further details, let me know! Here are some related questions you might consider:

  1. What is the significance of the z-score in statistics?
  2. How do you interpret a z-score of -1.5?
  3. What percentage of data falls within one standard deviation of the mean in a normal distribution?
  4. How can you convert a z-score back to a data value?
  5. What is the relationship between z-scores and probabilities in a normal distribution?

Tip: When analyzing z-scores, remember that negative values indicate a position below the mean, while positive values indicate a position above the mean.

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Math Problem Analysis

Mathematical Concepts

Statistics
Normal Distribution
Z-Scores

Formulas

z = (X - μ) / σ

Theorems

Properties of Normal Distribution
Z-Score Interpretation

Suitable Grade Level

Grades 9-12