The scores of your state’s high school seniors on the ACT college entrance examination in a recent year had mean and standard deviation . The distribution of scores is only roughly Normal.
What is the approximate probability that a single student randomly chosen from all those taking the test scores 27 or higher?
Now consider an SRS of 16 students who took the test. What are the mean and standard deviation of the sample mean score of these 16 students?
What is the approximate probability that the mean score of these 16 students is 27 or higher?
Which of your two Normal probability calculations in parts (a) and (c) is more accurate? Why?