Calculating percentile and standard deviations in curved grading system

Could someone please assist me with figuring this out?

In school, if all the classes taken fall in a curve and each class is weighted the same where 20% of the students receive an A (worth 4 points), 9% A- (3.7 points), 30% B+ (3.3 points), 22% B (3 points), 15% B- (2.7 points), and 4% C+ (2.3 points), how do you find the percentile of a 3.693 GPA? “A” is the highest grade possible and “C+” is the lowest grade possible. I have tried using a normal distribution curve to find the standard deviation, but that does not seem to be working. Thanks!

JStavely said:

In school, if all the classes taken fall in a curve and each class is weighted the same where 20% of the students receive an A (worth 4 points), 9% A- (3.7 points), 30% B+ (3.3 points), 22% B (3 points), 15% B- (2.7 points), and 4% C+ (2.3 points), how do you find the percentile of a 3.693 GPA? “A” is the highest grade possible and “C+” is the lowest grade possible. I have tried using a normal distribution curve to find the standard deviation, but that does not seem to be working. Thanks!

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This is a discrete probability distribution, number of students (y) as a function of grade (x). When you plot it, it doesn't look very "normal." You can calculate the mean and standard deviation, but they are not very useful in this case.

To find median and percentiles, make a table and/or plot of the cumulative distribution - that is, the sum of all students making up to the given score. Start at a score of 2.0, with the sum of students being 0. At 2.3 (or 2 1/3?) the sum is 4%. At 2.7 the sum is 19% . . . up to 100% at 4.0. The simplest way to interpolate the cumulative distribution is to draw straight line segments connecting the points on the cumulative plot. For a score measured on the horizontal axis, the vertical position is the percentile. For instance to find the median, interpolate between B and B+. To find the percentile corresponding to 3.693, interpolate between A- and A.