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

Answer

To find the lowest score Elena could have received, we will follow these steps:

**Step 1: Understand the given information.**
- Mean score (μ) = 60
- Standard deviation (σ) = 15
- We need to find the lowest score within 2 standard deviations of the mean.

**Step 2: Calculate the range of scores within 2 standard deviations of the mean.**
- The formula for the lower limit within 2 standard deviations is:
\[ \text{Lower limit} = \text{Mean} - 2 \times \text{Standard Deviation} \]

**Step 3: Substitute the values into the formula.**
- Substitute the mean and standard deviation into the formula:
\[ \text{Lower limit} = 60 - 2 \times 15 \]

**Step 4: Perform the multiplication.**
- Calculate \(2 \times 15\):
\[ 2 \times 15 = 30 \]

**Step 5: Subtract the result from the mean.**
- Now, subtract 30 from 60:
\[ 60 - 30 = 30 \]

**Step 6: Conclusion.**
- Therefore, the lowest score Elena could have received is **30**.