Amanda and ben are in different statistics classes. amanda scores a 15 on a quiz. her classmates have a mean of 20 and the standard deviation of 5 on the quiz. ben scores a 70 on a quiz. his classmates have a mean of 75 and a standard deviation of 10 on the quiz. who did better relative to their classmates?

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.