Step 1 :Given values are margin of error \(E = 0.02\), Z-score for 95% confidence level \(Z = 1.96\), and proportion of population \(p = 0.0372\).
Step 2 :We need to calculate the sample size using the formula \(n = \frac{{Z^2 \cdot p \cdot (1-p)}}{{E^2}}\).
Step 3 :Substitute the given values into the formula, we get \(n = \frac{{(1.96)^2 \cdot 0.0372 \cdot (1-0.0372)}}{{(0.02)^2}}\).
Step 4 :Calculate the above expression to get the value of \(n\).
Step 5 :Round up \(n\) to the nearest integer.
Step 6 :The number of adults that must be surveyed now is \(\boxed{344}\).