This problem has been hauting me for over a week. It has to dowith probability.

Question

This problem has been hauting me for over a week. It has to dowith probability. Sarah and Charlie are college freshman taking PSY 101 fromProfessor Jones and Professor Smith, respectively. Sarah recievedan 82 on her research methods test, while Charlie got a 98 onProfessos Smith's test. Sarah was upset with herself for what sheconsidered a very poor performance, while Charlie was quite pleasedwith himself. Then, both professors shared their means and standarddeviations of the tests with their classes. The standard deviationin Sarah's class was 2.14, with a mean of 78. The standarddeviation for Charlie's class was 18, with a mean of 80. Explainwhy Sarah is now feeling much better about her 82, and Charlie isconsiderably more humble. Any hint, clue, or explanation will be greatly appreciated.THANKS in advance! This problem has been hauting me for over a week. It has to dowith probability. Sarah and Charlie are college freshman taking PSY 101 fromProfessor Jones and Professor Smith, respectively. Sarah recievedan 82 on her research methods test, while Charlie got a 98 onProfessos Smith's test. Sarah was upset with herself for what sheconsidered a very poor performance, while Charlie was quite pleasedwith himself. Then, both professors shared their means and standarddeviations of the tests with their classes. The standard deviationin Sarah's class was 2.14, with a mean of 78. The standarddeviation for Charlie's class was 18, with a mean of 80. Explainwhy Sarah is now feeling much better about her 82, and Charlie isconsiderably more humble. Any hint, clue, or explanation will be greatly appreciated.THANKS in advance!

Explanation / Answer

Well Sarah got a 82 and her class had an average of 78 and a standard deviation of 2.14. So Sarah is 1.86 standard deviations about the average which means that she is close to being in the upper 5% of her class. Charlie on the other hand is only .272 standard deviations above the mean so that means a lot of students did as well as he did and he is not that special.

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