You are a middle school principal and your 100 eighth-graders are about to take a national standardized test. The test is designed so that the mean score is m = 400 with a standard deviation of s = 70. Assume the scores are normally distributed.

a. What is the likelihood that one of your eighth-graders, selected at random, will score below 375 on the exam?

b. Your performance as a principal depends on how well your entire group of eighth-graders scores on the exam. What is the likelihood that your group of 100 eighth-graders will have a mean score below 375?