Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. Required:
a. What is the probability Professor Elderman’s class of 36 has a class average below 78?
b. Professor Elderman offers his class of 36 a pizza party if the class average is above 80. What is the probability that he will have to deliver on his promise?
c. What is the probability that a class of 36 students will have an average greater than 70 on Professor Elderman’s final exam?
d. What is the probability that a class of 15 students will have a class average greater than 70 on Professor Elderman’s final exam?
e. What is the probability that a randomly selected student in the class will score greater than 70 on Professor Elderman’s final exam?