The interval x ± S encompasses what proportion of data _______________?
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Answer: C. 68.27%
Explanation
The empirical rule states that normal distributions follow predictable spread percentages. One standard deviation above and below the mean captures the central core of data. Therefore the interval x plus or minus s encompasses approximately 68.27 percent of data. Also known as the sixty eight ninety five ninety nine point seven rule in statistics. Two standard deviations capture roughly ninety five point four five percent of observations. Three standard deviations encompass nearly all data points within a normal distribution.
Quality control engineers use these percentage intervals to set acceptable manufacturing limits. Educators analyze standardized test scores using normal distribution spread percentages. Financial risk managers apply these confidence intervals to forecast potential portfolio losses. Forty nine point four five percent underestimates the actual central coverage percentage. Ninety five point four five percent represents the interval spanning two standard deviations. Ninety nine point seven three percent represents the interval spanning three standard deviations.
- Subject
- Mathematics
- Category
- Statistics
- Topic
- —
- Difficulty
- medium
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