Question 1200310: Dwayne and Lloyd began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Dwayne took a test in Science and earned a 78.6, and Lloyd took a test in Math and earned a 65.5. Use the fact that all the students' test grades in the Science class had a mean of 73.5 and a standard deviation of 10.4, and all the students' test grades in Math had a mean of 62.8 and a standard deviation of 11.1 to answer the following questions.
Calculate the z-score for Dwayne's test grade.
Calculate the z-score for Lloyd's test grade.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
The z-score formula is
z = (x - mu)/sigma
In the numerator we're computing how far the score x is from the mean (mu)
The numerator is negative if x is below mu. This leads to a negative z-score.
The numerator is positive if x is above mu. This leads to a positive z-score.
Dividing that result over sigma tells us how far we are from the mean in terms of standard deviation (sigma) units.
Doing this computation standardizes each test score to allow for comparison.
Let's calculate the z-score for Dwayne.
z = (x - mu)/sigma
z = (78.6-73.5)/10.4
z = 0.49038461538461
z = 0.49
Do the same for Lloyd.
z = (x - mu)/sigma
z = (65.6 - 62.8)/11.1
z = 0.25225225225226
z = 0.25
Summary:
Dwayne: z = 0.49
Lloyd: z = 0.25
Therefore, Dwayne performed better on his test compared to Lloyd, since Dwayne has the higher z-score.
He is further to the right on the normal distribution scale.
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