The distribution of scores on a recent test closely followed a Normal distribution with a mean of 22 points and a standard deviation of 4 points.
A What proportion of the students scored at least 25 points on this test?
B. What is the 31st percentile of the distribution of test scores.
C. The teacher wants to transform the test scores so that they have an
approximately Normal distribution with a mean of 80 points and a standard
deviation of 10 points. To do this, she will use a formula of the form:
new score = a +b(old score) . Find the values of a and b that the teacher
should use to transform the distribution of test scores.
D. Before the test, the teacher gave a review assignment for homework. The
maximum score on the assignment was 10 points. The distribution of scores on
this assignment had a mean of 9.2 and a standard deviation of 2.1 points. Would
it be appropriate to use a Normal distribution to calculate the proportion of
students who scored below 7 points on this assignment? Explain.