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Example Questions
Example Question #1 : Z Scores
In a normal distribution, if the mean score is 8 in a gymnastics competition and the student scores a 9.3, what is the z-score if the standard deviation is 2.5?
Write the formula to find the z-score. Z-scores are defined as the number of standard deviations from the given mean.
Substitute the values into the formula and solve for the z-score.
Example Question #1 : Z Scores
Suppose a student scored a on a test. The mean of the tests are , and the standard deviation is . What is the student's z-score?
Write the formula for z-score where is the data, is the population mean, and is the population standard deviation.
Substitute the variables.
The z-score is:
Example Question #2 : Z Scores
Suppose Bob's test score is 50. Determine the z-score if the standard deviation is 3, and the mean is 75.
Write the formula for z-scores. This tells how many standard deviations above the below the mean.
Substitute the known values into the equation.
The z-score is:
Example Question #2 : 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:
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. 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. The mean of the exam grades is 66 and the standard deviation is 3. What is the z-score?
Write the formula for z-scores. 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:
Example Question #13 : Z Scores
Sarah scored an 8.5 out of ten on her gymnastics floor routine. 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. Z-scores are indicators of how many standard deviations above or below the mean.
Substitute the known values.
The answer is:
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, is the mean, and is the standard deviation.
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