Students in a representative sample of $69$ second$-$year students selected from a large university in England participated in a study of academic procrastination. Each student in the sample completed the Tuckman Procrastination Scale, which measures procrastination tendencies. Scores on this scale can range from $16$ to $64,$ with scores over $40$ indicating higher levels of procrastination. For the $69$ second$-$year students in the study at the university, the sample mean procrastination score was $41\mathrm{.}00$ and the sample standard deviation was $6\mathrm{.}86.$

$($a$)$

Construct a $95\%$ confidence interval estimate of $��,$ the population mean procrastination scale for second$-$year students at this college. $($Round your answers to three decimal places.$)$