To determine how many scores fall within two standard deviations of the mean, we first need to calculate the range of scores that fall within this interval.
The mean is given as \( \bar{x} = 0.45 \) and the standard deviation as \( \sigma = 0.13 \).
We calculate the lower and upper bounds of the scores within two standard deviations of the mean:
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Lower bound: \[ \text{Lower bound} = \bar{x} - 2\sigma = 0.45 - 2(0.13) = 0.45 - 0.26 = 0.19 \]
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Upper bound: \[ \text{Upper bound} = \bar{x} + 2\sigma = 0.45 + 2(0.13) = 0.45 + 0.26 = 0.71 \]
Now, we need to count the number of students whose scores fall between 0.19 and 0.71 (inclusive).
Given the options:
- 77
- 96
- 86
- 58
Without the actual table of scores, I cannot definitively say which option is correct. You would need to check how many student scores fall between 0.19 and 0.71 in the provided data.
If you can provide the actual scores, I can help to count them within the specified range.