Question

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?

Answer 1

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.