Chapter P, Section 5, Exercise 168 Curving Grades on an Exam A statistics instru
ID: 3322176 • Letter: C
Question
Chapter P, Section 5, Exercise 168 Curving Grades on an Exam A statistics instructor designed an exam so that the grades would be roughly normally distrt uted with mean 76 and standard deviation -8. Unfortunately, a nre aarm with ten minutes to go in the exam made it difficult for some students to finish. When the instructor graded the exams, he found they were roughly normally distributed, but the mean grade was 62 and the standard deviation was 20. To be fair, he decides to "curve" the scores to match the desired N (76, 8) distibution. To do this, he standardizes the actual scores to 2-scores using the N (62, 20) distribution and then "unstandardizes those scores to shift to N (76, 8) What is the new grade assigned for a student whose oniginal score was 47? Round your answer to the nearest integer New score How about a student who originally scores an 87 Round your answer to the nearest integer New scorem Show All xx hw4.po Screen Shot 2017--pmExplanation / Answer
Answer to the question is as follows:
a.
Original score is 47
First we find the Z-score of 47 as :
Z = (47-62)/20 = -.75
Now, we will Unstandardize the scores and hence,
The new score for the new normal score is : Mean + Z*Sigma = 76+(-0.75*8) = 70
b.
If the original score is 87, then the
New score is Z = (87-62)/20 = 1.25
Now, we will Unstandardize the scores and hence,
The new score for the new normal score is : Mean + Z*Sigma = 76+(1.25*8) = 86