In order to understand who did better relative to the class, you need to find and compare the Z-scores (considering that the grades are normally distributed).
The Z-score can be found by the formula:
z = (X - m) / σ
where:
X = grade
m = mean
σ = standard deviation
For Amanda:
z = (15 - 20) / 5
= -1.00
For Ben:
z = (70 - 75) / 10
= -0.50
Looking at a standard normal table, we find:
P(z < -1.00) = 0.15866
P( z < -0.50) = 0.30854
Therefore, the probability to have a grade lower than Anna's in her class is around 16%, while the probability to have a grade lower than Ben's in his class is around 31%.
Hence, Ben did better relative to his class.
