Question: Curving Grades on an Exam A statistics instructor designed an exam so that the grades would be roughly normally distributed with mean=76 and standard deviation=12.

Curving Grades on an Exam

A statistics instructor designed an exam so that the grades would be roughly normally distributed with mean=76 and standard deviation=12. Unfortunately, a fire alarm 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 was62and the standard deviation was16. To be fair, he decides to "curve" the scores to match the desiredN(76,12) distribution. He standardizes the actual scores toz-scores using theN(62,16) distribution and then "unstandardizes" thosez-scores to shift toN(76,12).

What is the new grade assigned for a student whose original score was48and for a student whose original score was 87?

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