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.
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A data value located 0.7 standard deviations below the mean has a z-score of:
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A data value located 2.5 standard deviations above the mean has a z-score of:
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The mean of the distribution has a z-score of:
If you have any questions or need further details, let me know! Here are some related questions you might consider:
- What is the significance of the z-score in statistics?
- How do you interpret a z-score of -1.5?
- What percentage of data falls within one standard deviation of the mean in a normal distribution?
- How can you convert a z-score back to a data value?
- 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
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