A telecommunications company wants to estimate the proportion of households that would purchase an additional telephone line if it were made available at a substantially reduced installation cost. Data are collected from a random sample of

500 households. The results indicate that 190 of the households would purchase the additional telephone line at a reduced installation cost. Complete parts​ (a) and​ (b) below.

Construct a 99% confidence interval estimate for the population proportion of households that would purchase the additional telephone line.