Respuesta :
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
[tex]Z =\frac{x -\mu}{\sigma}[/tex]
[tex] = \frac{3.85 -3.1}{0.4}[/tex]
Z =1.875
for Maria
GPA = 3.80
Mean of her school GPA = 3.05
Standard deviation = 0.2
[tex]Z =\frac{x -\mu}{\sigma}[/tex]
[tex] = \frac{3.80 -3.05}{0.2}[/tex]
Z =3.750
therefore z score for Maria is higher than Stephanie
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 [tex]X = 3.85, \mu = 3.1, \sigma = 0.4[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.85 - 3.1}{0.4}[/tex]
[tex]Z = 1.875[/tex]
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 [tex]X = 3.8, \mu = 3.05, \sigma = 0.2[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.8 - 3.05}{0.2}[/tex]
[tex]Z = 3.75[/tex]
Maria has the higher z score, so she has the higher GPA when compared to each of their schools.
