A statistics instructor designed an exam so that the grades would be roughly normally distributed with mean μ=75 and standard deviation σ=10. 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 was 62 and the standard deviation was 18. To be fair, he decides to “curve” the scores to match the desired N(75, 10) distribution. To do this, he standardizes the actual scores to z-scores using the N(62, 18) distribution and then “unstandardizes” those z-scores to shift to N(75, 10). What is the new grade assigned for a student whose original score was 47? How about a student who originally scores a 90?
