Can you show me step by step how to calculate this in a easy way$--$ Part two. Complete solution

$($a$)$ On the first semester of a year, $232$ students took the final exam in a course of statistics.

$141$ students passed the exam. Considering the set of students taking the exam as a

random sample, find a $95\%$ confidence interval for the passing rate $($i$.$e$.$ the proportion of

students passing the exam$).(5$p$.)$

$($b$)$ On the second semester of the year, $261$ students took the final exam of the course. $139$

students passed the exam. Considering the set of students taking the exam as a random

sample, find a $95\%$ confidence interval for the passing rate. $(5$p$.)$

$($c$)$ Assuming that the sets of students taking the exam each semester are independent of each

other, find a $95\%$ confidence interval for the difference of the passing rate between the

first and the second semester of the year. $(5$p$.)$

$($d$)$ Assuming that all $493$ students taking the exam during the year are independent of each

other and that the passing rate is equal to $0\mathrm{.}5,$ find the $($approximated$)$ probability that the

number of students passing the exam is larger than $280.($Hint: What is the distribution

of the number of students passing the exam?$)(5$p$.)$