Question: In 2007, the New England Patriots (an American football team) had a banner year, winning all 16 regular season games. In these 16 games, their points were: 38, 38, 38, 34, 34, 48, 49, 52, 24, 56, 31, 27, 34, 20, 28, and 38. Despite this obvious success, their fans were still a bit overconfident going into the playoffs. The consensus among fans was that they would average 50 points per game in the playoffs.
Plus, their fans were 95% sure that they would be within five points of this number (45 to 55). Illustrate the dimensions of their overconfidence. (For the purposes of this question, assume the Patriots participated in four playoff games.)