A statistics professor gave an exam and he found that the scores were normally d

Question

A statistics professor gave an exam and he found that the scores were normally distributed with a mean of 40 and a standard deviation of 10. a. If he curves the scores by adding 35 to each grade, what is the new mean? What is the new standard deviation? b. Is it fair to curve by adding 35 to each grade? Why or why not? c. If the grades are curved so that grades of B are given to scores above the bottom 70% and below the top 10%, find the numerical limits for a grade of B. d. Which method of curving the grades is fairer: Adding 35 to each original score or using the method given in part c? Explain.

Explanation / Answer

Let X be the Statistics scores

X is N (40,10)

a) If mean is added by 35. then new mean

=old mean +35

=75

New std dev = same

= 10

b) It is fair as the shape will not be affected by adding 35 to each score

c) Grade B lies between 70% and 90%

Z score for these would be 0.525 and 1.28

Hence x score would be

between

(Mean +0.525 * std dev , Mean +1.28*std dev)

= (45.25, 52.8)

d) Using method in part c is better as it gives a comparison between scores.

If 35 is added to each score, percentile or grade is not going to be affected at all.

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