Answer: 91.04%

## Explanation **Given:** - Mean (μ) = 80 - Standard deviation (σ) = 24 - We want P(32 ≤ X ≤ 116) **Standardize the values:** - Lower bound: z₁ = (32 - 80) / 24 = -48 / 24 = **-2** - Upper bound: z₂ = (116 - 80) / 24 = 36 / 24 = **1.5** **Using standard normal distribution:** - P(Z ≤ 1.5) = 0.9332 - P(Z ≤ -2) = 0.0228 - P(-2 ≤ Z ≤ 1.5) = 0.9332 - 0.0228 = **0.9104** **Convert to percentage:** - 0.9104 × 100% = **91.04%** **Verification:** - Option D: 91.04% ✓ - This represents the area under the normal curve between 2 standard deviations below the mean and 1.5 standard deviations above the mean - Approximately 95.44% of data falls within ±2σ, and 86.64% falls within ±1.5σ, so 91.04% is reasonable for the asymmetric interval [-2σ, +1.5σ]

Author: LeetQuiz Editorial Team