Question

1. Professor Heinz 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 69 and a standard deviation of 19. Use an appropriate normal transformation to Calculate the probability that a class of 36 students will have an average greater than 60 on Professor Heinz's final exam.

2. Professor Heinz 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 69 and a standard deviation of 19. Calculate the probability that a class of 36 students will have an average greater than 60 on Professor Heinz's final exam.

Answer 1

Solution:

Given:

Mean =

Standard Deviation =

Sample size = n = 36

Part 1) Use an appropriate normal transformation to Calculate the probability that a class of 36 students will have an average greater than 60 on Professor Heinz's final examination.

Since sample size n = 36 is large , we can use Central limit theorem which states that for large sample size n ,
sampling distribution of sample mean is approximately normal with mean of sample means:

and standard deviation of sample means is:

Thus normal transformation to Calculate the probability that a class of 36 students will have an average greater than 60 on Professor Heinz's final examination is given by:

Part 2) Calculate the probability that a class of 36 students will have an average greater than 60 on Professor Heinz's final examination.

that is: find:

Look in z table for z = -2.8 and 0.04 and find corresponding area.

P( Z< -2.84) = 0.0023

thus