Question

6.18 ACT scores of high school seniors. The scores
of your state’s high school seniors on the ACT
college entrance examination in a recent year had
mean m 5 22.3 and standard deviation s 5 6.2. The
distribution of scores is only roughly Normal.
(a) What is the approximate probability that a single
student randomly chosen from all those taking the test
scores 27 or higher?(b) Now consider an SRS of 16 students who took the
test. What are the mean and standard deviation of the
sample mean score x of these 16 students?
(c) What is the approximate probability that the mean
score x of these 16 students is 27 or higher?
(d) Which of your two Normal probability calculations
in parts (a) and (c) is more accurate? Why?

Answer 1