A standardized test has a mean score of 500 points with a standard deviation of 100 points. Five students' scores are shown below.Adam: 575 Beth: 690 Carlos:750 Doug:280 Ella: 440Which of the students have scores within two standard deviations of the mean?Group of answer choicesCarlos, DougAdam, Beth, Carlos, EllaAdam, BethAdam, Beth, Ella
Question
A standardized test has a mean score of 500 points with a standard deviation of 100 points. Five students' scores are shown below.Adam: 575 Beth: 690 Carlos:750 Doug:280 Ella: 440Which of the students have scores within two standard deviations of the mean?Group of answer choicesCarlos, DougAdam, Beth, Carlos, EllaAdam, BethAdam, Beth, Ella
Solution
To answer this question, we first need to calculate the range of scores that fall within two standard deviations of the mean.
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The mean score is 500 and the standard deviation is 100.
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Two standard deviations would be 2 * 100 = 200.
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Therefore, scores that fall within two standard deviations of the mean would be in the range of 500 - 200 = 300 to 500 + 200 = 700.
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Now, we compare each student's score to this range:
- Adam: 575 (within the range)
- Beth: 690 (within the range)
- Carlos: 750 (outside the range)
- Doug: 280 (outside the range)
- Ella: 440 (within the range)
So, the students who have scores within two standard deviations of the mean are Adam, Beth, and Ella. Therefore, the correct group of answer choices is "Adam, Beth, Ella".
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