A certain professor always seeks to have a curve inline with university standard

Question

A certain professor always seeks to have a curve inline with university standards. At his new university, the grade distribution across all courses is 45% A's, 35% B's, 18% C's and 2% NCs. In this professor's classes, the whole grade for the course is determined by a final exam of 218 points that has a historical distribution with a mean of 176 points and SD of 16.

What percentage of exam points does a student need to achieve the historical mean? Show all work. What should the numerical cut-off's of the course be? Justify by showing work. Evaluate these cut-offs in terms of the percentage of points earned on the exam.

Do these cut-offs match your intuition about what grades mean? Please provide an explaination.

Explanation / Answer

Given,

The grade distribution  45% A's, 35% B's, 18% C's and 2% NCs

Exam points = 218

mean = 176

standard deviation = 16

For a normal distribution, percentage of exam points does a student need to achieve the historical mean

176/218 * 100 = 0.807*100 = 80.7%

The distribution lies bewteen upper and lower control limits of normal distribution

If A,B,C are considered as passing

Since last 2% is considered as NCs

p(Z) = 0.02

Z score is = -2.05 (from Z table)

Z = (X-U)/s

-2.05 = ( X - 176) / 16

X = 176 - 32.8

= 153.2

So, the person should score minimum 153.2 inorder to pass

153.2/ 218 * 100 = 70.3

yes the grades that are prepared As, Bs, Cs, NCs are for the people whose marks distribution is normally distribution with mean = 176 abd SD = 16, but the actual percentage of pass and actual percentage of A doesnot have a big difference

Getting an average mark impiles scoring 80%, passing the test implies scoring 70% is likely to not scaled so closed in real situations

Hence the standard deviation should be large

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