Final answer:
The margin of error can be calculated using the formula Margin of Error = Critical Value * Square Root[(p*(1-p))/n]. By rearranging the formula and solving for n, we can calculate the margin of error for the given average proportion and confidence level. Plugging in the values, we find the margin of error to be approximately 0.098.
Step-by-step explanation:
The margin of error can be calculated using the formula:
Margin of Error = Critical Value (Z for a 95% confidence level) * Square Root[(p*(1-p))/n]
Given that the average proportion of distracted drivers is 35% and the margin of error is 9%, we can substitute these values into the formula to find the critical value:
0.09 = Z * Square Root[(0.35*(1-0.35))/n]
Since we don't have the sample size (n), we cannot directly solve for the critical value or margin of error. However, we can rearrange the formula and solve for n:
n = (Z^2 * p * (1-p)) / (Margin of Error)^2
Plugging in the known values, we get:
n = (Z^2 * 0.35 * (1-0.35)) / 0.09^2
At a 95% confidence level, the critical value (Z) is approximately 1.96. Substituting this value into the formula, we can solve for n:
n = (1.96^2 * 0.35 * (1-0.35)) / 0.09^2
After calculating n, we can then find the margin of error by plugging the values into the original formula:
Margin of Error = 1.96 * Square Root[(0.35*(1-0.35))/n]