The expression e^(-3)(1+3+3^2/2!+3^3/3!+3^4/4!) equals the cumulative probability of 4 arrivals during an interval for which the average number of arrivals equals 3.
Here's a step-by-step explanation:
1. Recognize that the given expression represents the cumulative probability for a Poisson distribution.
2. Identify the average number of arrivals (λ) as 3, which is the exponent in the e^(-3) term.
3. Recognize that the terms inside the parentheses correspond to the Poisson probability mass function (PMF) for k=0, 1, 2, 3, and 4 arrivals.
4. Since the expression sums up the probabilities for k=0 to k=4, it represents the cumulative probability of 4 arrivals.
5. In summary, the expression represents the cumulative probability of 4 arrivals during an interval where the average number of arrivals is 3.