SOLUTION: Which of the following exam grades has a better relative position?
a.) A grade of 43 on a algebra test with x̄=40 and s=3
b.) A grade of 75 on a geometry test with x̄=72 and s=
Algebra.Com
Question 1194419: Which of the following exam grades has a better relative position?
a.) A grade of 43 on a algebra test with x̄=40 and s=3
b.) A grade of 75 on a geometry test with x̄=72 and s=5
Show full solution, thank you!
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!
The z score formula is
z = (x - mu)/sigma
where,
x = raw score
mu = mean
sigma = standard deviation
I'll treat each xbar as mu, and each s as sigma
For part A, we have
x = 43
mu = 40
sigma = 3
So,
z = (x - mu)/sigma
z = (43-40)/3
z = 3/3
z = 1
which is the z score to part A.
A z score of 1 means we're exactly 1 standard deviation above the mean.
Positive z scores are above the mean, while negative z scores are below the mean.
For part B, we have this z score
z = (x - mu)/sigma
z = (75 - 72)/5
z = 3/5
z = 0.6
We can see that the z score in part A is larger; therefore, the exam grade in class A is in a better relative position to the entire class.
Answer: Choice A.
RELATED QUESTIONS
Need some help
Exam Grades, Which if these grades has a better relative position?... (answered by stanbon)
Which score has a higher relative position,
a score of 40 on a test for which... (answered by Theo,ewatrrr)
Which of the following exam scores is better relative to other students enrolled in the... (answered by ikleyn)
Santos and Casey began arguing about who did better on their tests, but they couldn't... (answered by math_tutor2020)
A math student has a 100 homework average and test grades of 99, 100, and 97. The... (answered by math_helper,Theo)
Which score have the highest relative position:
a score of 47.4 on a test for... (answered by ewatrrr)
A student's grade in a course is the average of 4 test grades and a final exam that is... (answered by stanbon)
A student's grade in a course is the average of 4 test grades and a final exam that is... (answered by Alan3354,rothauserc)
A student's grade in a course is the average of 4 test grades and a final exam that is... (answered by josgarithmetic)