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:

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:

The z score is given by:

If we use this we got:

Let Y the random variable that represent the scores for his friend, and for this case we know that:

The z score is given by:

If we use this we got:

So then the correct answer for this case is:

B) Our student, Z= 1.50; his friend, Z=2.00.

The correct option is option a. an extra variable that could explain result differences between groups.

Step-by-step explanation:

Confusion variables, also called third variables, are variables that the investigator did not control or did not eliminate and that damage the internal validity of an experiment, that is, the degree to which the results are valid.

The dependent and independent variables are the two main variables of any experiment or investigation. The independent is one that changes or is controlled to study its effects on the dependent variable. The dependent is that variable that is investigated and measured.

Confusion variables may cause the investigator to analyze the results incorrectly. The results may show a false correlation between dependent and independent variables.

So the correct option is option a. an extra variable that could explain result differences between groups.

This is because this additional variable that was not controlled or taken into account during the experimental study modifies the result. And the other groups that conducted the experiment and took into account the variable will have different results because they take into account other independent variables.