Answer: 5.59%

## Explanation This is a Poisson distribution problem where: - Average calls per hour (λ) = 2 - Time period = 8 hours - Total average calls in 8 hours = λ_total = 2 × 8 = 16 - We want P(X = 20) The Poisson probability formula is: \[ P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!} \] Where: - λ = 16 (average calls in 8 hours) - k = 20 (number of calls we want) \[ P(X = 20) = \frac{e^{-16} \cdot 16^{20}}{20!} \] Calculating this: - e^{-16} ≈ 1.125 × 10^{-7} - 16^{20} ≈ 1.208 × 10^{24} - 20! ≈ 2.433 × 10^{18} \[ P(X = 20) ≈ \frac{(1.125 × 10^{-7}) × (1.208 × 10^{24})}{2.433 × 10^{18}} ≈ 0.0559 \] Therefore, the probability is approximately 5.59%, which matches option A.

Author: LeetQuiz Editorial Team