[Probability and Statistics] A survey of 100 randomly selected people from city A regarding the safest mode of transportation found that 20 people chose express buses. Using this result, a 95\% confidence interval for the proportion of people who chose express buses was found to be $[ a , b ]$. For city B, a 95\% confidence interval is to be constructed for the proportion of people who think express buses are the safest mode of transportation based on a random sample of $n$ people. Find the minimum value of $n$ such that the maximum allowable sampling error of this confidence interval is at most $\frac { b - a } { 2 }$. [4 points]
[Probability and Statistics] A survey of 100 randomly selected people from city A regarding the safest mode of transportation found that 20 people chose express buses. Using this result, a 95\% confidence interval for the proportion of people who chose express buses was found to be $[ a , b ]$. For city B, a 95\% confidence interval is to be constructed for the proportion of people who think express buses are the safest mode of transportation based on a random sample of $n$ people. Find the minimum value of $n$ such that the maximum allowable sampling error of this confidence interval is at most $\frac { b - a } { 2 }$. [4 points]