[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

A final examination at Podunk University is constructed so

that the test scores are approximately normally distributed, with parameters [math]\mu[/math] and [math]\sigma[/math]. The instructor assigns letter grades to the test scores as shown in Table (this is the process of “grading on the curve”).

Grading on the curve.

Test Score	Letter grade
[math]\mu + \sigma \lt x[/math]	A
[math]\mu \lt x \lt \mu + \sigma[/math]	B
[math]\mu - \sigma \lt x \lt \mu [/math]	C
[math]\mu - 2\sigma \lt x \lt \mu - \sigma[/math]	D
[math]x \lt \mu - 2\sigma[/math]	F

What fraction of the class gets A, B, C, D, F?