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
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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.
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