CompTIA Data+ (DA0-002)Data AnalysisMedium
A data analyst calculates the mean score of a certification exam to be 75 with a standard deviation of 10. Assuming the scores are normally distributed, what percentage of test-takers would be expected to score between 65 and 85?
- AApproximately 99.7%
- BApproximately 50%
- CApproximately 68%
- DApproximately 95%
Show answer & explanationAnswer & explanation
Correct answer: C. Approximately 68%
The Empirical Rule (or 68-95-99.7 Rule) states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. Scores between 65 and 85 are (75 - 10) and (75 + 10), which is exactly one standard deviation below and above the mean.
Why the other options are wrong
- A. 99.7% of data falls within three standard deviations of the mean (75 ± 30, or 45 to 105).
- B. 50% would be below the mean, not within one standard deviation.
- D. 95% of data falls within two standard deviations of the mean (75 ± 20, or 55 to 95).
Empirical Rule (68-95-99.7 Rule)
A rule stating that for a normal distribution, nearly all data falls within three standard deviations of the mean.
- Approx. 68% of data within 1 standard deviation (μ ± 1σ).
- Approx. 95% of data within 2 standard deviations (μ ± 2σ).
- Approx. 99.7% of data within 3 standard deviations (μ ± 3σ).
Memory trick: NORMAL bell, 68-95-99.7 is the RULE!