Answer:
The number of randomly selected students that must be surveyed is 385.
Option (B) is true.
Explanation:
To determine the number of randomly selected students that must be surveyed, we can use the formula:
n = (Z^2 * p * (1 - p)) / E^2
Where:
n = sample size
Z = Z-score corresponding to the desired confidence level (97% = 1.97)
p = estimated proportion (0.5, assuming maximum variability)
E = margin of error (0.015)
Plugging in the values, we get:
n = (1.97^2 * 0.5 * (1 - 0.5)) / 0.015^2
n ≈ 384.57
Since we cannot have a fraction of a student, we round up to the nearest whole number.
Therefore,
Option (B) is true.