Chapter 5, Section 1, Exercise 040 SHOW HINT LINK TO TEXT Chapter 5, Section 1,

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Chapter 5, Section 1, Exercise 040

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Chapter 5, Section 1, Exercise 040

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Curving Grades on an Exam

A statistics instructor designed an exam so that the grades would be roughly normally distributed with mean and standard deviation . 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 and the standard deviation was . To be fair, he decides to ‘‘curve” the scores to match the desired distribution. To do this, he standardizes the actual scores to -scores using the distribution and then ‘‘unstandardizes” those -scores to shift to .

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

Round your answer to the nearest integer.

new score

How about a student who originally scores an ?

Round your answer to the nearest integer.

new score

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Explanation / Answer

Here original score was 49

so Z value

Z = (49 - 62)/18 = -0.7222

so it will be changed to the new distributionn

so new score

X = 75 - 0.7222 * 12 = 66.33 (66)

Original score = 85

Z = (85 - 62)/18 = 1.2778

so New score

Y = 75 + 1.27778 * 12 = 90.33 (90)

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