Inquiries to a service desk arrive at random, independently of one another, at an average of 3 per hour, and the number arriving in one hour follows a Poisson distribution. Taking e⁻³ ≈ 0.0498, which of the following is closest to the probability that exactly 2 arrive in a given hour?

Answer: C. 0.224

For a Poisson distribution with mean λ, the probability of k events is P(k) = λᵏ × e^(−λ) ÷ k!. With λ = 3 and k = 2, P(2) = 3² × e⁻³ ÷ 2 = 4.5 × 0.0498 ≈ 0.224. The Poisson distribution describes how many times a rare event occurs in a fixed time or area, and it is also used for the number of defects on a wafer.

• A. e⁻³ ≈ 0.050 is the probability that none arrive, P(0).
• B. 3 × e⁻³ ≈ 0.149 is the probability that exactly one arrives, P(1).
• C. Correct. 3² × e⁻³ ÷ 2! ≈ 0.224.