Question 1200310
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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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