All senior high school students in a certain state take a test on which the statewide results are approximately normally distributed with mean 60 and standard deviation 10. A random selection of sixty-four test results is chosen.

a. What is the probability that the average of the sixty-four test results will be below 57?

b. What is the probability that a school with sixty-four senior students will score an average result of less than 57? POLI967