Question

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 76 and a standard deviation of 12. Use an appropriate normal transformation to calculate the probability that a class of 36 students will have an average greater than 72 on Professor Heinz's final exam.

Answer 1

0.97725

Explanation:

Given that 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 76 and a standard deviation of 12.

i.e.
`\mu = 76\\\sigma = 12\\\bar x = 72\\n = 36`

Std error of mean = sigma/sqrt n = 2

Thus the sample mean is N(76,2)

Required probability = probability that a class of 36 students will have an average greater than 72 on Professor Heinz's final exam.

=
`P(X>72)\\= P(Z>-2)\\=0.97725`