Robin Dunbar, a leading anthropologist at Oxford University who studies social networks, has suggested that there is a magical number for social networks that humans can manage: any grouping larger than 150 people becomes overwhelming. With that in mind, a group of researchers at Facebook wanted to study more about how their average user manages their social networks. In particular they wanted to study the users with the highest friend counts to see how they managed. They took a random sample from users who were in the top 15% when their users were arranged according to their friend count. This study of these 225 Facebook users found a mean of 520 friends. Facebook knows from prior studies of their users that the standard deviation is 46. How large a sample of facebook users is needed in order to estimate with a 95% confidence interval of length 14.16 friends? 900 144 625 841 169