Question

Given the table of 100 sample proportions, how many samples fall within one standard deviation of the mean?
The standard deviation is σ=0.11 and the mean is
x
ˉ
=0.40.
A. 66
B. 59
C. 95
D. 74

Answer 1

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:

1. **Lower bound**:
\[
\bar{x} - \sigma = 0.40 - 0.11 = 0.29
\]

2. **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.**