Question
Determine which score corresponds to the higher relative position. Who’s score is better: Jane got a score of 82 on her math test with a mean of 70 and a standard deviation of 8, and Jim got a score of 82 on his math test with a mean of 75 and a standard deviation of 4? (Show work) a) Both scores have the same relative position. b) Jane’s score, 82 c) Jim’s score, 82 Work:
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Answer to a math question Determine which score corresponds to the higher relative position. Who’s score is better: Jane got a score of 82 on her math test with a mean of 70 and a standard deviation of 8, and Jim got a score of 82 on his math test with a mean of 75 and a standard deviation of 4? (Show work) a) Both scores have the same relative position. b) Jane’s score, 82 c) Jim’s score, 82 Work:
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To determine which score corresponds to the higher relative position, we can calculate the z-scores for both Jane and Jim's scores.
For Jane's score:
z = \dfrac{x - \mu}{\sigma} = \dfrac{82 - 70}{8} = \dfrac{12}{8} = 1.5
For Jim's score:
z = \dfrac{x - \mu}{\sigma} = \dfrac{82 - 75}{4} = \dfrac{7}{4} = 1.75
Since Jim's z-score is higher than Jane's z-score, Jim's score of 82 corresponds to the higher relative position.
Therefore, the answer is:
c) Jim's score, 82
For Jane's score:
For Jim's score:
Since Jim's z-score is higher than Jane's z-score, Jim's score of 82 corresponds to the higher relative position.
Therefore, the answer is:
c) Jim's score, 82
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