SAT verbal scores are normally distributed with a mean of 430 and a standard deviation of 120 (based on data from the College Board ATP). Randomly selected SAT verbal scores are obtained from the population of students who took a test preparatory course from a training school. Assume that this training course has no effect on test scores.
a. If one of the students is randomly selected, find the probability that he or she obtained a score greater than 440.
b. If 100 students of an SAT preparation course achieve a sample mean of 440, does it seem reasonable to conclude that the course is effective because the students perform better on the SAT?