A disaster analyst estimates that the time (in hours) between emergency calls during a hurricane follows an exponential distribution with a mean of 20 hours. What is the probability that the next emergency call occurs within 10 hours?

Thu, 30 Apr 2026 10:31:42 +0000

**What Is the Probability That the Next Emergency Call Arrives Within 10 Hours? Understanding Risk in Disaster Response with Exponential Analysis** When hurricane season approaches each year, emergency planners face a quiet but pressing question: How soon will the next alert call come? A disaster analyst estimates that emergency response calls during major storms follow an exponential distribution with a mean of 20 hours. This statistical insight reveals not just patterns—but critical information for resource readiness. In a moment of heightened focus on resilience and preparedness, this seemingly technical detail shapes how communities anticipate and respond to disaster. The exponential distribution models waiting times between rare but impactful events, ideal for emergency calls that occur sporadically after initial storm impacts. While 20 hours is the average interval between calls, the real question often lies in a shorter window—Can the next emergency call happen within 10 hours? This matters not only for immediate ambulance dispatches or shelter staffing but also for public awareness and response design. ### Why This Model Matches Real-Hurricane Communication