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?
Accepted Solution
A:
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%.