Respuesta :
Answer:
[tex] z= \frac{85-70}{10}=1.5[/tex]
[tex] z= \frac{45-35}{5}=2[/tex]
So then the correct answer for this case is:
B) Our student, Z= 1.50; his friend, Z=2.00.
Step-by-step explanation:
Assuming this complete question:
A statistics student wants to compare his final exam score to his friend's final exam score from last year; however, the two exams were scored on different scales. Remembering what he learned about the advantages of Z scores, he asks his friend for the mean and standard deviation of her class on the exam, as well as her final exam score. Here is the information:
Our student: Final exam score = 85; Class: M = 70; SD = 10.
His friend: Final exam score = 45; Class: M = 35; SD = 5.
The Z score for the student and his friend are:
A) Our student, Z= -1.07; his friend, Z= -1.14.
B) Our student, Z= 1.50; his friend, Z=2.00.
C) Our student, Z= 1.07; his friend, Z= -1.14.
D) Our student, Z= 1.07; his friend, Z= 1.50
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution
Let X the random variable that represent the scores for our student, and for this case we know that:
[tex] E(X)= \mu =70, SD_X=\sigma=10[/tex]
The z score is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we use this we got:
[tex] z= \frac{85-70}{10}=1.5[/tex]
Let Y the random variable that represent the scores for his friend, and for this case we know that:
[tex] E(Y)= \mu =35, SD_Y=\sigma=5[/tex]
The z score is given by:
[tex]z=\frac{y-\mu}{\sigma}[/tex]
If we use this we got:
[tex] z= \frac{45-35}{5}=2[/tex]
So then the correct answer for this case is:
B) Our student, Z= 1.50; his friend, Z=2.00.
