Answer: μ ± 2σ.
- A μ ± σ
- B μ ± 2σ
- C μ ± 3σ
- D μ ± 1.5σ
Correct answer: B. μ ± 2σ
Explanation: Empirical 68-95-99.7 rule: P(μ−σ < X < μ+σ) ≈ 68%, P(μ−2σ < X < μ+2σ) ≈ 95%, P(μ−3σ < X < μ+3σ) ≈ 99.7%. Standard normal Z-table gives P(−1.96 < Z < 1.96) = 95%, confirming μ ± 2σ.
In a perfectly normal (bell-shaped) distribution, mean, median, and mode all coincide at the centre; about 68% of data falls within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3 - the empirical rule used to judge how typical or extreme a value is.
Concept context
Mean, median, mode, standard deviation, and data interpretation