1. **Problem statement:** We are given that the number of new visitors to a website in one hour follows a Poisson distribution with mean $\lambda = 2.8$. We want to find the probability that zero new visitors arrive in one hour. 2. **Formula:** The probability mass function (PMF) of a Poisson random variable $X$ with mean $\lambda$ is given by: $$P(X = k) = \frac{\lambda^k e^{-\lambda}}{k!}$$ where $k$ is the number of events (visitors) and $e$ is Euler's number (approximately 2.71828). 3. **Apply the formula for $k=0$:** $$P(X=0) = \frac{2.8^0 e^{-2.8}}{0!} = \frac{1 \cdot e^{-2.8}}{1} = e^{-2.8}$$ 4. **Calculate the value:** $$e^{-2.8} \approx 0.0608$$ 5. **Interpretation:** The probability that zero new visitors arrive in any given hour is approximately 0.0608. **Final answer:** $$\boxed{0.0608}$$