A lecturer wishes to "grade on the curve". The students' marks seem to be normally distributed with mean 70 and standard deviation 8. If the lecturer wants to give 20% A's, what should be the threshold between an A grade and a B grade?
Ten days later this is probably worth an answer:
A normal distribution has about 20% of its distribution more than 0.842 standard deviations above the mean; using the cumulative distribution of standard normal $\Phi$, $$\Phi(0.842) \approx 0.8$$ so the threshold should be about $70 + 8\times 0.842 \approx 76.7$.
I do wonder slightly why the lecturer would do this instead of just giving an A to the top 20% of students.