To determine how many samples fall within one standard deviation of the mean, we can use the empirical rule (68-95-99.7 rule) which states that approximately 68% of the data in a normally distributed dataset falls within one standard deviation of the mean.
Given:
- Mean \( \bar{x} = 0.40 \)
- Standard deviation \( \sigma = 0.11 \)
Calculating the range that falls within one standard deviation of the mean:
-
Lower bound: \[ \bar{x} - \sigma = 0.40 - 0.11 = 0.29 \]
-
Upper bound: \[ \bar{x} + \sigma = 0.40 + 0.11 = 0.51 \]
Thus, we are looking for the number of samples that fall between 0.29 and 0.51.
Since we have 100 samples, and approximately 68% of the samples will fall within this range:
\[ 0.68 \times 100 = 68 \]
Thus, the number of samples that fall within one standard deviation of the mean is approximately 68.
However, looking at the options provided:
A. 66
B. 59
C. 95
D. 74
The closest answer would be A: 66.