What percentage of scores in a normal distribution fall within two standard deviations of the mean (between μ - 2σ and μ + 2σ)?
Answer and explanation
Correct answer: D. Approximately 95.4%
- Step 1: In a Gaussian normal distribution, the empirical rule dictates spread. Step 2. Two standard deviations capture 95.44% of total area under the curve. Answer: Approximately 95.4%. Why not the others: 68.2% corresponds to one standard deviation; 89.0% applies to Chebyshev's inequality for arbitrary distributions; 99.7% corresponds to three standard deviations.
Practise more Educational Statistics, Percentiles and Assessment Metrics.
Free questions with an explanation for every one, and full timed Ghana Teacher Licensure Examination mock tests.
More Educational Statistics, Percentiles and Assessment Metrics questions
- A class of 10 students scored the following marks out of 20: 8, 12, 12, 14, 15, 15, 15, 17, 18, 19. What is the mode?
- Nine pupils recorded test scores of 45, 50, 52, 58, 60, 65, 70, 78, 85. What is the median score of the group?
- A student scored at the 75th percentile in a national standardized literacy assessment. How is this interpreted?
- In a symmetric bell-shaped normal distribution of 1,000 student scores with mean 50 and standard deviation 10, what percentage falls between…
- The mean mark of 20 boys was 65, while the mean mark of 30 girls was 75. What is the combined mean mark of all 50 pupils?
- If the variance of test scores in a class test is 36, what is the standard deviation?