5. On a recent statewide math test, the raw score average was 56 points with a standard deviation of 18. If the scores were normally distributed and 16,000 students took the test, answer the following questions.
(a) What percent of students scored below a 20 on
the test? (5 pts)
(b) How many students scored more than a 38? (5)
(c) If the state would like to scale the test so that a
90% would correspond to a raw score that one
and a half standard deviations above the mean,
what raw score is needed for a 90%? (5)
(d) How many of the 16,000 students receive a scaled
score greater than a 90%? (5)
(1) What should the raw passing score be set at so
that no more than the students fail? (5)
(e) The state would like no more than 17 of the
16000 students to fail the exam. What percent of
the total does the 275 represent? Round to the
nearest tenth of a percent. (5)