Two students, stephanie and maria, want to find out who has the higher gpa when compared to each of their schools. stephanie has a gpa of 3.85, and her school has a mean gpa of 3.1 and a standard deviation of 0.4. maria has a gpa of 3.8, and her school has a mean of 3.05 and a standard deviation of 0.2. who has the higher gpa when compared to each of their schools?

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.

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step-by-step explanation:

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