To determine the proportion of residents in a certain city who have experience using the central park, $n$ residents of the city were randomly sampled and surveyed. The result showed that 80\% had experience using the central park. Using this result, the 95\% confidence interval for the proportion of residents in the entire city who have experience using the central park is $[ a , b ]$. When $b - a = 0.098$, find the value of $n$. (Here, when $Z$ is a random variable following the standard normal distribution, calculate using $\mathrm { P } ( | Z | \leq 1.96 ) = 0.95$.) [4 points]
To determine the proportion of residents in a certain city who have experience using the central park, $n$ residents of the city were randomly sampled and surveyed. The result showed that 80\% had experience using the central park. Using this result, the 95\% confidence interval for the proportion of residents in the entire city who have experience using the central park is $[ a , b ]$. When $b - a = 0.098$, find the value of $n$. (Here, when $Z$ is a random variable following the standard normal distribution, calculate using $\mathrm { P } ( | Z | \leq 1.96 ) = 0.95$.) [4 points]