Question

To calculate grades in her statistics course, Professor Clark converted the raw scores on all four exams to z-scores. Each student’s final course grade was then based on his or her highest z score. Sara’s raw scores are shown below along with the mean and standard deviation for each of the four exams.

Exam	Raw Score	mean	stDev
1	50	45	10
2	30	30	10
3	25	20	2
4	25	20	3

Which exam did Sara do the best on? _____________

Which exam did Sara do the worst on? _____________

Answer 1

Solution:

Sara’s raw scores are shown below along with the mean and standard deviation for each of the four examinations:

Examination	Raw Score	mean	Std Dev
1	50	45	10
2	30	30	10
3	25	20	2
4	25	20	3

We have to find z score for each raw score.

z score formula:

z score for 1st examination raw score = 50 is:

z score for 2nd examination raw score = 30 is:

z score for 3rd examination raw score = 25 is:

z score for 4th examination raw score = 25 is:

Thus we get:

Which examination did Sara do the best on?

Since z score for Examination 3 is 2.50 which is highest among all other scores, thus Sara did best on Examination 3.

Which examination did Sara do the worst on?

Since z score for Examination 2 is 0.00 which is lowest among all other scores, thus Sara did worst on Examination 2.