POSSIBLE POINTS: 3
What z-score did I get?
SKILL 3.C
Analyzing the effect of transformations
PROBLEM:
In a large introductory statistics class, the distribution of scores on a recent test follows an approximately Normal distribution with a mean of 82.4 and a standard deviation of 5.1. Let x be the test score for a randomly selected student. To test the students' grasp of the material, the teacher cleverly decides to convert all the scores to z-scores and then report these values to students. If Z is the z-score for the randomly selected student, then
Z=(x-82.4)/(5.1)
(a) Find the mean of Z.
(b) Calculate and interpret the standard deviation of Z.
POSSIBLE POINTS:3
What z-score did I get?
SKILL3.C
Analyzing the effect of transformations
PROBLEM:
In a large introductory statistics class, the distribution of scores on a recent test follows an approximately Normal distribution with a mean of 82.4 and a standard deviation of 5.1.Let Xbe the test score for a randomly selected student.To test the students'grasp of the material, the teacher cleverly decides to convert all the scores to z-scores and then report these values to students.If Z is the z-score for the randomly selected student,then
Z=x-82.4/5.1
aFind the mean of Z
(b) Calculate and interpret the standard deviation of Z