Answer:
Maria has the higher z score, so she has the higher GPA when compared to each of their schools.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Between Stephanie and Maria, whoever has the higher zscore has the higher GPA when compared to each of their schools.
Stephanie
Stephanie has a GPA of 3.85, and her school has a mean GPA of 3.1 and a standard deviation of 0.4. So we have
. So



Maria
Maria has a GPA of 3.8, and her school has a mean of 3.05 and a standard deviation of 0.2. This means that
. So



Maria has the higher z score, so she has the higher GPA when compared to each of their schools.