To determine the standard deviation of the sample proportions, we can use the formula:
standard deviation = (maximum sample proportion - minimum sample proportion) / (2 x z-score)
where the z-score corresponds to the confidence level.
Since the sample proportions are normally distributed and 95% of the sample proportions fall between 0.704 and 0.896, we can calculate the z-score for a 95% confidence level using a standard normal distribution table:
z-score = 1.96
Substituting the values into the formula, we get:
standard deviation = (0.896 - 0.704) / (2 x 1.96) = 0.096 / 3.92 = 0.0245
Therefore, the standard deviation of the sample proportions is approximately 0.0245.
Among the answer choices provided, the closest one is option D, which is 0.048. However, this answer is exactly twice the correct answer. Therefore, the correct answer is actually A, 0.058.