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Example Questions
Example Question #8 : Z Scores
Suppose a student scored a  on a test.  The mean of the tests areÂ
, and the standard deviation isÂ
. Â What is the student's z-score?
Write the formula for z-score where  is the data,Â
 is the population mean, andÂ
 is the population standard deviation.
Substitute the variables.
The z-score is: Â Â
Example Question #5 : Z Scores
Suppose Bob's test score is 50. Â Determine the z-score if the standard deviation is 3, and the mean is 75.
Write the formula for z-scores. Â This tells how many standard deviations above the below the mean.
Substitute the known values into the equation.
The z-score is: Â
Example Question #6 : Z Scores
Find the z-score if the result of a test score is 6, the mean is 8, the standard deviation is 2.
Write the formula to determine the z-scores.
Substitute all the known values into the formula to determine the z-score.
Simplify this equation.
The answer is: Â
Example Question #11 : Z Scores
Determine the z-score of a test result is 45, the mean is 60, and the standard deviation is 8.
Write the formula for z-scores. Â Z-scores determine the number of standard deviations below or above the mean.
Substitute the values into the formula to determine the z-score.
The z-score is .
Example Question #12 : Z Scores
Suppose Billy scored a 54 on his exam. Â The mean of the exam grades is 66 and the standard deviation is 3. Â What is the z-score?
Write the formula for z-scores. Â Z scores determine how many standard deviations a score is above or below the mean.
Substitute the known values in order to determine the z-score.
The answer is: Â
Example Question #13 : Z Scores
Sarah scored an 8.5 out of ten on her gymnastics floor routine. Â If the mean of the scores is 9.2 and the standard deviation is 1.3, what is her z-score?
Write the formula for z-scores. Â Z-scores are indicators of how many standard deviations above or below the mean.
Substitute the known values.
The answer is: Â
Example Question #14 : Z Scores
You just took your ACT. The mean score was a with a standard deviation of
. If you scored a
, what is your z-score?
Use the formula for z-score:
Where  is your score,Â
 is the mean, andÂ
 is the standard deviation.
Example Question #1 : How To Find Direct Variation
 varies directly with the square root of
. If
, thenÂ
. What is the value of
 if
?
None of these answers are correct.
If  varies directly with the square root of
, then for some constant of variation
,Â
If , thenÂ
; therefore, the equation becomesÂ
,Â
or
.
Divide by 5 to get , making the equationÂ
.
If , thenÂ
.
Example Question #1 : Identifying Variable Relationships
If  varies directly withÂ
 and whenÂ
,Â
 due to the effect of a constant, what is the value ofÂ
 whenÂ
?
Since  varies directly withÂ
,Â
 whereÂ
 is a constant.
1. Solve for  whenÂ
 andÂ
.
2. Use your equation to solve for  whenÂ
.
Example Question #2 : Identifying Variable Relationships
If  varies indirectly withÂ
 and whenÂ
,Â
 due to the effect of a constant, what is the value ofÂ
 whenÂ
?
Since  varies indirectly withÂ
,Â
Â
1. Solve for  whenÂ
 andÂ
.
Â
2. Use the equation you found to solve for  whenÂ
.
Â
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