Consider yourself to be a middle school principal. Your 115 eighth-graders are about to take a national standardized test. The test is designed so that the mean score is 600 with a standard deviation of 80. Assume the test scores are normally distributed.
a. What is the likelihood that one of your eighth-graders, selected at random, will score below 580 on the exam?
b. Your performance as a principal depends on how well your entire group of eight-graders scores on the exam. What is the likelihood that your group of 115 eighth-graders will have an average score below 580?