Question

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.

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

0.5675

0.1587

0.8413

Cannot be determined.

Answer 1

Class size of 36 ( >30) suggests we can use the Central Limit Theorem for distribution of average class scores.

Given historical class scores have mean=76 and std deviation=12, the random variable X representing the average class scores over years can be considered to follow a normal distribution, X ~ N(76, 12²).

Now, we need P(X < 78)

Now Z-score of 78 = (78 - 76) / 12 = 1/6 = 0.1667

P(X<78) = P(Z < 0.1667) 0.5675  (can be looked up from Z-score probability table)