Design and optimization of many network applications, services, protocols, and routing protocols can be improved with delay-related measurement for a better operation over the Internet. Many experimental delay measurements have been performed on predetermined end-to-end connections with a less number of hosts compared to our study. This study aims to investigate up-to-date round-trip delay time measurement results over the Internet through pinging random IPv4 addresses from three vantage points located in the United States, Turkey, and Japan. Considering different time periods in a day and in consecutive 5 years, we performed a large-scale round-trip delay time analysis study by sending more than 300 million ICMP requests to randomly chosen IPv4 addresses. Approximately, 55 million unique Internet hosts replied to ICMP requests and were evaluated for the analysis. The results show that 90\% of IP hosts accomplish their ICMP communication in less than 0.4 s. Mostly the propagation time on backbone links constitutes the larger part of total round-trip delay time. Distribution fitting test results demonstrate that RTTs of distributed hosts around the world could be modeled with multimodal distribution functions. Wakeby distribution function gives best results for modeling RTTs with two different modes according to the Kolmogorov--Simirnov test statistics. Our study also gives perspective about how packet delay values would be, when a message is broadcasted all over the world. Another significant finding is that it gives a point of view where to locate servers to provide a fast Internet service all over the world via Internet.