Question

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?

Answer 1

Answer:

z score for Maria is higher than Stephanie

Step-by-step explanation:

for Stephanie

GPA = 3.85

Mean of her school GPA = 3.1

Standard deviation = 0.4

$Z =\frac{x -\mu}{\sigma}$

  $= \frac{3.85 -3.1}{0.4}$

Z =1.875

for Maria

GPA = 3.80

Mean of her school GPA = 3.05

Standard deviation = 0.2

$Z =\frac{x -\mu}{\sigma}$

  $= \frac{3.80 -3.05}{0.2}$

Z =3.750

therefore z score for Maria is higher than Stephanie

Answer 2

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 $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 $X = 3.85, \mu = 3.1, \sigma = 0.4$. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{3.85 - 3.1}{0.4}$

$Z = 1.875$

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 $X = 3.8, \mu = 3.05, \sigma = 0.2$. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{3.8 - 3.05}{0.2}$

$Z = 3.75$

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