Respuesta :
Answer:
Jennifer has the higher zscore, so she did better than Andy on the midterm exam.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the zscore.
The z-score formula is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In which: X is the grade, [tex]\mu[/tex] is the mean value of all the grades and [tex]\sigma[/tex] is the standard deviation of the grades.
Between Andy and Jennifer, whoever has the highest Zscore did better on their midterm exam.
Andy:
Andy's score on the Spanish exam was 22.5 points. The distribution of Spanish exam scores was normal (bell-shaped) with an average score of 20 points (out of 25 points possible) and a standard deviation of 1.97 points. So [tex]X = 22.5, \mu = 20, \sigma = 1.97[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{22.5 - 20}{1.97}[/tex]
[tex]Z = 1.269[/tex]
Jennifer
Jennifer's score the the math exam was 72 points. The distribution of math exam scores was uniform over the range of 20 to 80 points, with a mean of 50 points and a standard deviation of 17.32 points. So [tex]X = 72, \mu = 50, \sigma = 17.32[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{72 - 50}{17.32}[/tex]
[tex]Z = 1.2702[/tex]
Jennifer has the higher zscore, so she did better than Andy on the midterm exam.
