Netflix is considering a new romcom $($romantic comedy$)$ series. Before making a final decision, the producers design an experiment to estimate the proportion of viewers who would watch the series. A random sample of $1,160$ viewers was selected and asked to watch the first two episodes. After viewing the episodes, $725$ viewers indicated they would watch the new series. $($Round your answers to $3$ decimal places.$)$

a$.$ Estimate the value of the population proportion of people who would watch the new series.

b$.$ Develop a $99\%$ confidence interval for the population proportion of people who would watch the new series.