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Which statement is true of normally distributed data?
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True statements (key properties) about data that are normally distributed:
- The distribution is symmetric and bell-shaped.
- Mean = median = mode (all equal).
- It is fully described by its mean (μ) and standard deviation (σ).
- About 68% of values fall within ±1σ of the mean, ~95% within ±2σ, and ~99.7% within ±3σ (the empirical rule).
- The distribution is continuous with tails that extend to infinity.
- Linear combinations of independent normal variables are normal; the sum of independent normals is normal.
- Skewness = 0 and (population) kurtosis = 3 (excess kurtosis = 0).
If you have specific answer choices, paste them and I’ll tell you which is true.
- The distribution is symmetric and bell-shaped.
- Mean = median = mode (all equal).
- It is fully described by its mean (μ) and standard deviation (σ).
- About 68% of values fall within ±1σ of the mean, ~95% within ±2σ, and ~99.7% within ±3σ (the empirical rule).
- The distribution is continuous with tails that extend to infinity.
- Linear combinations of independent normal variables are normal; the sum of independent normals is normal.
- Skewness = 0 and (population) kurtosis = 3 (excess kurtosis = 0).
If you have specific answer choices, paste them and I’ll tell you which is true.
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