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 20 years, he finds that the scores have a mean of 76 and a standard deviation of 12.

1. What is the probability Professor Elderman’s class of 36 has a class average below 78?

2. 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?

3. What is the probability that a class of 36 students will have an average greater than 70 on Professor Elderman’s final exam?

4. What is the probability that a class of 15 students will have a class average greater than 70 on Professor Elderman’s final exam?

5. What is the probability that a randomly selected student in the class will score greater than 70 on Professor Elderman’s final exam?

Administrative assistants in a local university have been asked to prove their proficiency in the use of spreadsheet software by taking a proficiency test. Historically, the mean test score has been 74 with a standard deviation of 4. A random sample of size 40 is taken from the 100 administrative assistants and asked to complete the proficiency test.

What is the probability that the sample mean score is more than 75, the predetermined passing score?