Consider you are a designer for a social networking website and you have been sought to ensure that a video could be downloaded quickly for playback in the web browsers of site visitors (quick playback of videos would help attract and retain those visitors). By running experiments in the corporate offices, you determined that the amount of time, in seconds, that passes from first linking to the website until a video is fully displayed is a bell-shaped distribution with a mean download time of 7 seconds and standard deviation of 2 seconds. Using different web page designs, some download times of a video have been evaluated: if the standard deviation remained at 2 seconds, lowering the mean to 6 seconds would shift the entire distribution lower by 1 second. Thus, approximately 84% of the download times would be 8 seconds or less, and 95% of the download times would be between 2.08 and 9.92 seconds. Another change that could reduce long download times would be reducing the variation. For example, consider the case where the mean remained at the original 7 seconds but the standard deviation was reduced to 1 second. Again, approximately 84% of the download times would be 8 seconds or less, and 95% of the download times would be between 5.04 and 8.96 seconds.
Question 1 Review and evaluate these conclusions.
Page | 2 Also, to satisfy concerns of potential customers, the management has undertaken a research project to learn the amount of time it takes users to load a complex video features page. The research team has collected data (see the Excel file provided “Data Assignment 1.xls”) and has made some claims based on the assertion that the data follow a normal distribution. This is the internal report that documents the work of the team and their conclusions:
Question 2 Write the 5 Number Summary and draw the boxplot with the data provided.
Question 3 Can the collected data be approximated by a normal distribution? Justify and explain your answer in detail.
Question 4 Review and evaluate the conclusions made by the research team. Which ones are correct? Which ones are incorrect?
Question 5 If the mean could be improved by five seconds, how would the probabilities change?