1. State Police Academy graduates from a large graduating class have scored an average of 81.0 on a profi- ciency test, and the scores are normally distributed with a 5 8.5. Graduates are randomly paired and assigned to barracks throughout the state. Madeleine has scored 83.0 on the test. What is the probability that she will be paired with someone whose score was within 5.0 points of her own?
2. The trainer for a professional football team has found that, on the average, his team experiences 2.3 sprained ankles per 1000 game minutes. If a game lasts 60 minutes, and the number of game minutes between ankle sprains is exponentially distributed, determine the probability that the next ankle sprain will occur
a. during the team's next game.
b. sometime during the team's next ten games.
c. at the moment the 2-minute warning is sounded in the next game.