Step 1 :We are given that the desired margin of error (E) is 3.5% or 0.035, the Z-score for a 90% confidence interval (Z) is approximately 1.645, and since we don't know the proportion of snowboarders, we'll use the most conservative estimate, which is p = 0.5.
Step 2 :We want to find the sample size (n), so we can use the rearranged formula for the margin of error in a proportion: \(n = \frac{Z^2p(1-p)}{E^2}\).
Step 3 :Substituting the given values into the formula, we get: \(n = \frac{(1.645)^2 * 0.5 * 0.5}{(0.035)^2}\).
Step 4 :Calculating the above expression, we find that n is approximately 552.7.
Step 5 :Since we can't have a fraction of a person, we'll round up to the nearest whole number.
Step 6 :Final Answer: The required sample size to produce a margin of error of at most 3.5 percentage points with a 90% confidence interval is \(\boxed{553}\).