Multiple choice

The class mean score on a test was $60$, and the standard deviation was $15$. lf Elena's score was within $2$ standard deviations of the mean, what is the lowest score she could have received?

  1. $20$
  2. $30$
  3. $40$
  4. $50$
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B Correct answer
Explanation

Mean = 60, SD = 15. Two standard deviations = 2 * 15 = 30. Range = 60 +/- 30, which is [30, 90]. The lowest score is 30.

AI explanation

Using the empirical rule for normal distributions, a score within 2 standard deviations of the mean falls in the range calculated as mean plus or minus 2 times the standard deviation. The lower bound is calculated as 60 minus 2 multiplied by 15, which equals 60 minus 30. Therefore, the lowest possible score she could have received is 30.

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