Question

The University of Pittsburgh Medical (UPMS) School grades each class in the following manner:

All students whose score is plus or minus two standard deviations from the mean course score receive a grade of “Pass.”

Students whose score is above two standard deviations from the course mean receive a grade of “Pass with Distinction.”

And, students whose score is below two standard deviations from the course mean receive a grade of “Fail.” Course scores are always assumed to be normally distributed.

Approximately what percentage of medical students in each class receives a “Pass with Distinction”?

Answer 1

Let X denote the grades of a students from UPMS School.

Now, we are given that "course scores are always assumed to be normally distributed".

Thus, for some and some .

Now, we need to find the percentage of medical students in each class who receive a "Pass with distinction".

We are given in question that, "Students whose score is above two standard deviations from the course mean receive a grade of “Pass with Distinction”"

Thus, we get:

Thus, 2.275% of medical students in each class receive a "Pass with distinction" [ANSWER]

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