Question

Suppose your statistics instructor gave six examinations during the semester. You received the following exam scores (percent correct): 79, 66, 81, 85, 89, and 77. To compute your final course grade, the instructor decided to randomly select two exam scores, compute their mean, and use this score to determine your final course grade.

Compute the population mean. This is your average grade based on all of your grades. (Round your answer to 2 decimal places.)

Compute the population standard deviation. (Round your answer to 2 decimal places.)

How many difference scores could be calculated if your instructor decided to random sample two of your exam scores?

List all possible samples of size 2 and compute the mean of each. (Round your answers to 1 decimal place.)

Compute the mean of the sample means and the standard error of the sample means. (Round your answers to 2 decimal places.)

Applying the central limit theorem, if the instructor randomly samples two of your exam scores to compute an average as your final course grade, what is the probability your final course grade will be less than 79.50? What is the probability that your final course grade will be more than 79.50? (Round your answers to 1 decimal places.)

Answer 1

For the central limit theorem part, we have the column of sample means as our required data. Mean of that column is 79.5 and sample standard deviation of that is 4.717

Using Standard Normal approximation,

P(X<79.5) = P(Z<79.5-79.5/4.717) = P(Z<0) = 0.5

And probability that P(X>79.5) = 1- P(X<79.5) = 0.5