## Correct Answer: C. 180-220 This question tests the **68-95-99.7 rule** (empirical rule) of the normal distribution, a cornerstone of biostatistics taught in Indian medical schools. When data follows a normal distribution, approximately 68% of observations fall within **one standard deviation (±1 SD) of the mean**. Given mean = 200 and SD = 20, the range is: mean ± 1 SD = 200 ± 20 = 180–220. This rule is fundamental to understanding population distributions in epidemiological surveys, clinical trials, and public health assessments in India. The 68% figure is not arbitrary—it derives from the properties of the Gaussian curve and is empirically validated across large populations. In Indian public health contexts (e.g., nutritional surveys, disease screening programs), this rule helps identify "normal" versus "abnormal" values and set reference ranges for laboratory tests. The discriminating fact is that **68% corresponds to ±1 SD, not ±2 SD or ±3 SD**, which students often confuse under exam pressure. ## Why the other options are wrong **A. 190-210** — This range represents mean ± 0.5 SD (200 ± 10), which would capture only ~38% of the population, not 68%. This is a **trap for students who halve the SD value** or misremember the rule. It appears plausible because 190 and 210 are close to the mean, but the width is too narrow. **B. 170-230** — This range represents mean ± 1.5 SD (200 ± 30), which would capture approximately 86.6% of the population. This is a **common error when students confuse the 68% rule with the 95% rule** (±2 SD). The range is too wide for 68%. **D. 160-240** — This range represents mean ± 2 SD (200 ± 40), which captures approximately 95% of the population under the empirical rule. This is the **classic NBE trap**—students who remember '95%' instead of '68%' will select this. It tests whether the candidate knows the specific SD multiplier for 68%. ## High-Yield Facts - **68-95-99.7 rule**: In a normal distribution, 68% of data lies within ±1 SD, 95% within ±2 SD, and 99.7% within ±3 SD of the mean. - **±1 SD for 68%**: The discriminating multiplier is 1, not 0.5, 1.5, or 2—this is the most commonly confused concept in biostatistics exams. - **Reference ranges in Indian labs**: Clinical reference ranges (e.g., hemoglobin, glucose) are typically set as mean ± 2 SD to capture 95% of healthy populations, not 68%. - **Normal distribution assumption**: The empirical rule applies only when data is approximately normally distributed; skewed distributions (common in Indian nutritional surveys) may not follow this rule. - **Population vs. sample**: The question specifies 'population study'—use population parameters (μ, σ), not sample statistics (x̄, s). ## Mnemonics **68-95-99.7 Memory Hook** **1-2-3 rule**: 1 SD → 68%, 2 SD → 95%, 3 SD → 99.7%. Think '1-2-3' as the SD multiplier, then recall the percentages in order. Use this when you see any question asking for population ranges in normal distributions. **NBE Trap Detector** If the question gives you SD = 20 and mean = 200, **immediately calculate ±1 SD, ±2 SD, ±3 SD ranges** before looking at options. This prevents confusing 68% with 95% or 99.7%. ## NBE Trap NBE pairs the 68% figure with the 95% rule (±2 SD) to trap students who confuse the percentages. Option D (160–240, representing ±2 SD) is the classic distractor for candidates who remember "95%" instead of "68%"—a high-yield trap in Indian medical exams. ## Clinical Pearl In Indian public health screening programs (e.g., NRHM nutritional surveys, TB screening), reference ranges for "normal" are often set at mean ± 2 SD (95%) to minimize false positives, but understanding the 68% rule helps clinicians recognize that ~32% of healthy individuals will fall outside ±1 SD—a critical insight to avoid over-diagnosis in community surveys. _Reference: Park's Textbook of Preventive and Social Medicine, Ch. 10 (Biostatistics); Harrison's Principles of Internal Medicine, Ch. 7 (Statistical Interpretation of Data)_
Sign up free to access AI-powered MCQ practice with detailed explanations and adaptive learning.