A group of statistics students took a midterm exam. The class mean was 72 and th

Question

A group of statistics students took a midterm exam. The class mean was 72 and the standard deviation was 3.2. The instructor decided to "curve" the grades. Assuming that the distribution of grades was normal, the instructor decided to assign grades the following way: Students whose test grades are within 1/2 standard deviation of the class mean will receive C's. B's and D's will be given to scores from (and including) 1/2 standard deviation up to (and including) 1 1/2 standard deviations above and below the mean respectively. A's and F's will be given to scores above and below 1 1/2 standard deviations of the mean respectively. a). What percentage of students will receive each grade? A's: B's: C's: D's: F's: b). What grade would a student with a score of 70 make? c). What grade would a student with a score of 86 make? d). Devise a grading scale for the test. Values should be rounded to the nearest ones' place. Remember that no grades may exist in more than one category.

Explanation / Answer

mean =72 sd = 3.2 1/2 standard deviation of the class mean above and below: mean + (0.5)(3.2) = 72+(3.2)(0.5) = 73.6 mean - (0.5)(3.2) = 72-(3.2)(0.5) = 70.4 Therefore, students whose mean score is between 70.4 and 73.6 will receive a C. µ = 72 s = 3.2 standardize x to z = (x - µ) / s P( 70.4

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